







The volume of a berm 
20180604 

From Mike: Have a berm that is 700 long, 29 yall and needs a 20 top with 51 slope on one side and 31 slope in the other Answered by Penny Nom. 





The angles of a trapezoid 
20180414 

From Gautham: In trapezoid ABCD, sides AB and CD are parallel, \angle A = 2angle D, and angle C = 3angle B. Find angle A. Answered by Penny Nom. 





A trapezoid inscribed in a circle 
20170517 

From Kameron: I have been given a challenge problem that states that Diameter AB is drawn in a circle if 10 inch. Chords AC and BD are drawn so that each is of length 12inch and ACDB is a trapezoid. Find the height, in inches, of the trapezoid Answered by Penny Nom. 





The height of a isosceles trapezoid 
20170403 

From Riham: Hi
How can I find the height in an isosceles trapezoid if I have the measurements of all of its sides ?
Thank u in advance. Answered by Penny Nom. 





The volume of a trench 
20150311 

From Kim: A trench 60m long and 15m deep, 12m wide at the top and 8m wide at the bottom.How many cubic meters of earth have been removed? Answered by Penny Nom. 





Is a square a trapezoid? 
20150126 

From Katie: Can a trapezoid sometimes be a square? Answered by Penny Nom. 





A truncated, squarebased pyramid 
20141123 

From Hannah: A designer vase has the shape of a truncated, squarebased pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface
area of the vase. Answered by Penny Nom. 





A circle insubscribed in an isosceles trapezoid 
20131208 

From Bob: A circle is insubscribed in an isosceles trapezoid, with
parallel lengths of 8cm and 18cm.
What is the lengths of sloping edges and why? Answered by Robert Dawson. 





A sloped concrete wall 
20131030 

From Brad: We are planning on pouring concrete in a wall form that is sloped. One end is 73 inches tall, and it tapers to 24 inches tall over a distance of 348 inches. It is flat on bottom and sides and is 12 inches thick. Thanks. Answered by Penny Nom. 





A proof by contraposition 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, then x>=e. I understand the approach very well but I do not understand why if x=e then x>=e. If it is so then why not x=
Thanks in advance!'
Rahul. Answered by Penny Nom. 





A lot with a slope 
20120330 

From Carlos: I have a lot with a slope. On the right I need to bring it up 2', From that point to the left is 112' which at this point I need to bring it up 5' for it to be level . The distance front to back is 80'. What is the cubic yards of this area that I need to fill in. Answered by Harley Weston. 





A trapezoidal prism filled with sand 
20120312 

From Maria: could a Trapezoid that is 80 inches high with a 54 inch width top and a 89 inch width bottom and a 80 inch depth hold 58 cubic yards of sand? Answered by Robert Dawson. 





The end of a trough 
20111021 

From Lorraine: The vertical end of a trough has the following dimensions: width at top 4.4 ft., width at bottom 3.2 ft., depth 3.5 ft. Find the area at the end of the trough. Answered by Penny Nom. 





A trapezoid inscribed in a circle 
20111002 

From Greg: A trapezoid is inscribed within a circle.
The two interior angles who share the longest side are 70 and 80.
The arc whose chord is the longest side has a length of 120.
Find the other two interior angles of the trapezoid, and the other three arc lengths. Answered by Chris Fisher. 





A trapezoid 
20110802 

From Nazrul: How can I draw a trapezoid whose parallel sides and other two sides are given. Answered by Chris Fisher. 





A stained glass lamp 
20110725 

From Guy: Like Kay, I also work in stained glass, but in 3dimensions. I am
frequently asked to replicate lamp shades in stained glass where the
diameter of the top is different (narrower) from the diameter of the
bottom (which is wider). Some people want 5, 6, 7, 8, 10, 12, 16, ,,,
nsided shades. Is there a formula I can use to determine the width
of the sides using the angle, if I remember correctly, I think it's
called theta. In other words, is there a formula where I can plug
in the angle which describes the arc of the circle. For instance, if
someone asks for a 7 sided shade, plugging in 51.43 (360/7). I
could then use that to determine the width at the top and bottom
rings to create the appropriate trapezoids. I've visited a few sites
so the formula looks like its a function of sin & cos but they are
presented like proofs for teaching. Your site appears to want to
actually answer questions without making the inquirer feel stupid. Answered by Harley Weston. 





A circle is inscribed inside an isosceles trapezoid 
20110225 

From priyam: a circle is inscribed inside an isosceles trapezoid (with parallel sides
of length 18 cm and 32 cm) touching all its four sides.
find the diameter of the circle.
thanks for help!! Answered by Penny Nom. 





The height of the trapezoid 
20101201 

From Ryan: A trapezoid has an area of 10.5 cm squared and parallel sides that
measure 5.0 cm and 2.0 cm what is the height of the trapezoid Answered by Penny Nom. 





The sides of a trapezoid 
20101103 

From Bobbi: Isosceles Trapezoid base=60; two 45⁰angles at base, two 135⁰ angles at the top, vertical distance between base & top=16. What is the length of the top line and the two equal side lines? Answered by Penny Nom. 





A water trough 
20101022 

From Jasmine: A water trough is 8 m long and its crosssection is an isosceles
trapezoid which is 90 cm wide at the bottom and 120 cm wide
at the top, and the height is 30 cm. The trough is not full.
Give an expression for V , the volume of water in the trough in cm^3,
when the depth of the water is d cm. Answered by Stephen La Rocque. 





An isosceles trapezoid is inscribed in a circle 
20100406 

From Abby: An isosceles trapezoid whose bases have lengths 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid Answered by Penny Nom. 





The area of a trapezoid 
20100301 

From mariah: the height of a trapezoid is 6 centimeters. one of the bases is three times the height, and other base is four times the height . find the area of the trapezoid Answered by Penny Nom. 





The area of a trapezoid 
20100106 

From maureen: the question asks for the area of a trapezoid with parallel sides 5m and 6m and height of 2.5m
I have done it by dividing the trapezoid into 2 triangles and reach the same answer as my manual11.25 sq. m
My question...how would you illustrate this? I read this to mean to sets of parallel sides, which would mean it is a parallelogram and not a trapezoid.
Any suggestions? Answered by Robert Dawson. 





An isosceles trapezoid 
20091112 

From lyjah: what is parallel sides of an isosceles trapezoid measure 5cm and 11cm long.and
oneof the other sides also measures s5cn long what of the isosceles trapeziod Answered by Penny Nom. 





The Smythe family lot 
20090524 

From Shrima: We must determine the size of the lot. The Smythe family lot is 235ft
across the front and 212ft down the side and 254ft down the other side.
The sides of the lot are parallel to each other and perpendicular to the front.
The size of the lot is two dimensional measure therefore you need to find
the areaenclosed by the lot line.
Question:
What is the size of the Smythe lot including the unit? Answered by Penny Nom. 





A triangle inside a trapezoid 
20090406 

From rohan: i have a diagram with a triangle inside a trapezoid.trapezoid is PQRS ,
PQ being the line above and RS THE LINE BELOW.The area of this is 12.
If RS is twice PQ what is the area of PQS. Answered by Penny Nom. 





A quadrilateral with exactly 1 pair of parallel sides and no congruent sides 
20081210 

From alie: a quadrilateral with exactly 1 pair of parallel sides and no congruent sides is what? Answered by Robert Dawson. 





The diagonals of an isosceles trapezoid 
20081114 

From hazel: how to solve the diagonals of an isosceles trapezoid? what is the formula? Answered by Harley Weston. 





The area of a trapezoid 
20081104 

From kelsey: The area of a trapezoid is approximately 150cm2...the length is 26 cm, the
weight is 5cm...what is the height????
(show me the work that you did so i can understand) Answered by Penny Nom. 





The area of a trapezoid 
20080515 

From Ashley: what is the formula for area of a trapezoid Answered by Penny Nom. 





The fourth side of a property 
20080514 

From Penny: Property has 3 measurements and 2 angles and I want the altitude at a particular point. Corners are sw, nw, ne and se. 1 want the 4th saide measurement confirmed (we think 146.07') and the altitude measurement at 25' from sw (on the swse side)
The angles provided are interior at nw 67.38 degrees and the opposing corner se interior appears to be 68.58 degrees. the 3 sides with measurements are: sw to nw=54.07'. sw to se 146.07' and se to ne 53.57'. If you would help, we would really appreciate it. Thanks! Penny Answered by Harley Weston. 





An incorrect Babylonian formula 
20080310 

From Martin: Given the area of an isosceles trapezoid is 150, that the difference of its bases is 5 (that is b1  b2 = 5), and that its equal sides are 10 greater than twothirds of the sum of its bases (that is, s1 = s2 = 2/3(b1 +b2) + 10
Solve the problem using an incorrect Babylonian formula for the area of a trapezoid A = (b1 + b2)/2 x (s1 + s2)/2 Find the length of the sides of the isosceles trapezoid. Answered by Penny Nom. 





The area of a trapezium (trapezoid) 
20071105 

From Scott: How can we calculate this I do not understand?
A trapezium of area 126m2 has parallel sides of length 3m and 4m. How far apart are the parallel sides? Answered by Stephen La Rocque and Harley Weston. 





The area of a roof 
20070927 

From RANDY: I have an area of roof. It's in a sort of triangle.
it's 25' across the top
30' at each edge
86' across the bottom Answered by Stephen La Rocque. 





Are the diagonals of a trapezoid ever perpendicular? 
20070923 

From Amanda: Are the diagonals of a trapezoid ever perpendicular? Answered by Harley Weston. 





Subdividing a property into half acre parcels 
20070731 

From Pamela: We need to divide a large property with five sides and strange angles into 1/2 acre parcels from the top down. We want to know where along the eastern and western borders of the large property to make the divisions. Answered by Stephen La Rocque. 





More on quadrilateral shape names 
20070526 

From Don: If North Americans call a quadrilateral with no parallel sides a trapezium, is a kite merely a special type of trapezium? Can a rhombus be a kite? Answered by Walter Whiteley and Penny Nom. 





Is a square also a right trapezoid? 
20070524 

From Don: Is a square also a right trapezoid? Answered by Stephen La Rocque. 





Splitting a 5 acre piece of property 
20070125 

From John: I have a 5 acre piece of property that I wish to split into 5 individual 1 acre parcels. The 5 acre parcel 1s 660 feet in length and 330 feet in width. The first two parcels are 264'x165', but I am asking for help getting the perimeters of the last 3 lots, one of which is a irregular pentagon. All of the one acre parcels must have an area of 43,560 square feet each. Answered by Penny Nom. 





Are all rectangles trapezoids? 
20070105 

From Sarah: Are all rectangles trapezoids? Answered by Chris Fisher. 





A trapezoid with one right angle? 
20061209 

From Andre: How do you draw a trapezoid with one right angle? Answered by Stephen La Rocque. 





The name of a shape 
20061111 

From Valentina: I have a shape of 4 sides 3 are the same length (2cm each) and the other smaller (1.5cm) Answered by Chris Fisher. 





Area of a trapezium demonstration 
20060718 

From Karthik: how can u " SHOW THAT THE AREA OF THE TRAPEZIUM IS EQUAL TO HALF THE PRODUCT OF ITS ALTITUDE AND THE SUM OF ITS PARALLEL SIDES." in an Innovative And Creative way..... Answered by Stephen La Rocque. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





The area of a parallelogram 
20060312 

From Shayne: Is there a method of finding the area of a trapezium or/and parallelogram even if the height is not given? Could you also explain how to find the height? Answered by Penny Nom. 





The diagonals of a trapezoid 
20051111 

From Chris: Is there ever a case where the diagonals of a trapezoid bisect each other? Answered by Walter Whiteley. 





The diaonals of an isosceles trapezoid are congruent 
20050202 

From Daniel: I am currently unable to find a proof that the diaonals of an isosceles trapezoid are congruent. Might you happen to have one? Answered by Walter Whiteley. 





The area of a trapezoid 
20050115 

From Doak: What is the total acreage of a pieshaped piece of land that is:
146' f ront
85' back
246' each side
The front and back lines are fairly straight....a trapezoidal shape. Answered by Penny Nom. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





The area of a lot 
20040928 

From Stan: I own a parcel of land (lot 20) that is assessed at 9127.00 square feet and has a frontage of 99.90 feet according to the tax roll. I don't know how large my property actually is since I feel that the tax assessment and the survey map don't jive Answered by Harley Weston. 





Constructing a cone 
20040907 

From Steve: I am trying to build crayfish traps; one of the components is a cone shaped entry section.
The cone I want to make would be 12" in diameter at the base and 12" in height, from base to peak.
I need a formula to calculate the dimensions and a method of transferring the shape onto a flat piece of material.
Answered by Harley Weston. 





An isosceles trapezoid 
20040831 

From Bruce: An isosceles trapezoid with bases of lengths 12 and 16 is inscribed in a circle with a radius of 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid. Answered by Penny Nom. 





The trapezoidal rule 
20031231 

From Prashanth: I have a set of XY coordinates(say 49 points),I want to find the area enclosed by the curve joining them and the axes.I do not have an equation for the curve and I am not able to fit a curve given the points.I use the trapezoidal rule
(Y1+Y2/2)*(X2X1),
Is it right? can I do this with any other method? Answered by Penny Nom. 





Area of a trapezoid 
20030413 

From A road builder: My husband works with asphalt building roads. There are times when one end of the road will be (for example) 100ft wide the other end would be( for example) 200ft wide and he must figure the area in square feet. So far it has been a guessing game because he dosen't have the formula to figure the square feet. Answered by Penny Nom. 





A quadrilateral with 0 sets of parallel sides 
20011212 

From Jess: Ok well for quadrilaterals a parallelogram is a 4 sided figure with 2 sets of parallel sides and a trapezoid is a 4 sided figure with 1 set of parallel sides. So is there a name for a quadrilateral with 0 sets of parallel side? Answered by Chris Fisher. 





The median of a trapezoid 
20011001 

From Laura: Given: A (1,2) B (9,2) C (7,2) D (3,4) Find the endpoints of the median. Use exact values. Write the equation using the letters from the given trapezoid. Verify the theorem using algebra. Answered by Penny Nom. 





A Trapezium problem 
20001215 

From Ben: A trapezium has a perimeter of 22cm. The 2 parallel sides are such that the length of one is three times the length of the other. The nonparallel sides are equal. If the distance between the parallel sides is 4cm, find the lengths of the 4 sides. Answered by Claude Tardif. 





An Area 
20000626 

From Frank: Can you tell me what the sq. ft. are of and area measuring: __________58____________
 
 
 
 
 
76  70 
 
 
_____21________ 
Answered by Harley Weston. 





Putting in a pool 
20000316 

From Katie: If your digging a hole for a pool and the pool is: Length= 11m Width= 6m Sallow Depth= 1.1m graduating to 'Deep' Depth= 1.8m What is the volume of soil that will be taken out? And if a bobcat can excavate and remove 10m3 (qubed) of soil an hour how long will it take him to excavate the soil. Answered by Penny Nom. 





Two calculus problems 
19991213 

From Alan: I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. Answered by Harley Weston.






Universal Area 
19990408 

From Karen Richardson: I need a formula for area that works for a square, a rectangle, a parallelogram, a trapezoid, and a triangle. Answered by Jack LeSage, Chris Fisher and Harley Weston. 





A Kite 
19981007 

From Paul Scott: What is the mathematical term for the kite shape? Answered by Walter Whiteley. 





Isosceles trapezoid formula 
19980512 

From Donna McMullin: The teacher of Gifted and Talented Math has been trying to locate the formula for anisosceles trapezoid and we can't find it anywhere. Could it be the same formula for that of a parallelogram ? Please advise. Answered by Walter Whiteley. 





Two Inscribed Trapezoids 
19980127 

From James: A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to m/n, where m and n are relatively prime positive integers. Find m+n. Answered by Haragauri Gupta. 





The Area of a Trapezoid. 
19970507 

From Mary George: I am doing the area of trapezoids and mixed polygons and I was wondering if you can help me figure out this problem. A line segment drawn parallel to a leg of a right triangle divides the other leg into segments of 3cm and 6 cm and the hypotenuse into segments of 5cm and 10 cm. The two figures formed are a triangle and a trapezoid. Find the area of each. I would appreciate if you would email me back the solution. Answered by Harley Weston. 





Show that this construction yields a rhombus. 
19960616 

From LennyB: Hello, I have a problem. I doubt you can help me. If you have an isosceles trapezoid, and you connect the midpoints of the four sides of the isosceles trapezoid forming a quadrilateral, how do you prove that it's a rhombus in a 2 column proof?? Answered by Penny Nom. 

