







Quadrilateral ABCD is inscribed in a circle 
20170911 

From Joie: Quadrilateral ABCD is inscribed in a circle such that side DA is the diameter. AB=2m., BC=4m., CD=6m., angle BAD=75.93degrees. Find the area of the quadrilateral. Answered by Penny Nom. 





Quadrilateral 
20160614 

From Muhib: Is there a quadrilateral with 0 sets of parallel sides. Answered by Penny Nom. 





The area of a 4sided lot 
20160525 

From prasad: How to find area of a land whose sides are 41ft,33ft,32.3ft and 33.2 ft. Pl give me the formula and proof. Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20160205 

From Andrea: The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram. Answered by Penny Nom. 





A quadrilateral inside a square 
20160130 

From Subrahmanya: In a square ABCD of side 6 units P, Q are mid points of BC, CD respectively. The line segments BQ, DP intersect in R then find the area of the quadrilateral ABRD using only plane geometry. Answered by Chris Fisher. 





The area of a quadrilateral 
20150311 

From Joel: Diagonal ac of quadrilateral ABCD is 60cm and the lengths of perpendiculars to
It from the opposite vertices are 4.2cm and 5.8 cm find the area of the quadrilateral
ABCD Answered by Penny Nom. 





The area of a quadrilateral 
20140806 

From Rahul: find the area of the quadrilateral whose side measure9cm,40cm,28cm,15cm and in which the angle between the first 2 sides is a right angle Answered by Penny Nom. 





A cyclic quadrilateral 
20140328 

From Carly: Suppose ABCD is a cyclic quadrilateral, i.e A, B, C, and D are the points on a circle,
given in order going around the circle. Show that if we join each of A, B, C, and D to the orthocentre
of the triangle formed by the other three, then the resulting line segments all intersect in a common midpoint.
Thank you. Answered by Chris Fisher. 





The fourth side of a quadrilateral 
20140123 

From joanna: left vertical measurement 2560mm
right vertical measurement 1850mm
base horizontal measurement 1750mm
question  what will the 4th measurement be please.
using a scale drawing I make it approx 1900mm but require an accurate measurement
regards
Joanna Answered by Penny Nom. 





The area of a quadrilateral 
20131221 

From khushboo: Find the area of quadrilateral pqrs in which
angle QPS=90°,PQ=12cm, PS=9cm, QR=8cm and SR=17cm.
(Hint: PQRS has two parts) 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. 





The area of a quadrilateral 
20120421 

From Rajat: calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''. Answered by Penny Nom. 





If a parallelogram is a cyclic quadrilateral then it is a rectangle 
20120201 

From Kim: Show that if a parallelogram is a cyclic quadrilateral then it is a rectangle.
Hint: Observe that in a parallelogram ABCD we always have Triangle ABC is congruent to Triangle CDA. Answered by Robert Dawson and Chris Fisher. 





A cyclic quadrilateral 
20110815 

From Tim: Hi! I've been working on this for a while and I'm quite stuck. If anyone can help that would be great.
The sides BC and AD of a quadrilateral ABCD are parallel. A circle meets the side AB at B and E and the side CD at C and F. Prove that the quadrilateral AEFD is cyclic. Answered by Chris Fisher. 





Exactly two lines of symmetry 
20100411 

From debbie: i am looking for a quadrilateral with exactly two lines of symmetry. please help! thank you. Answered by Tyler Wood. 





A quadrilateral with 4 known sides and 1 known angle 
20100319 

From samuel: Name: Samuel
Status: Student
I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.
By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).
However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).
Is there any simpler way? Answered by Robert Dawson and Harley Weston. 





An irregular quadrilateral 
20091029 

From riya: what is irregular quadrilateral? Answered by Penny Nom. 





A cyclic quadrilateral 
20090123 

From Murtaza: Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic. Answered by Robert Dawson and Chris Fisher. 





The area of a quadrilateral shape 
20090119 

From craig: how do u work out the area of a quadrilateral shape Answered by Robert Dawson. 





A quadrilateral with two pairs of congruent sides 
20081210 

From nicole: what is the name of a figure that has 2 sides that measure 25 feet each and 2 sides that measure 10 feet each? Answered by Robert Dawson. 





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 area of a quadrilateral 
20080911 

From Mike: How do I find the area of a quadrilateral that has one sloped side? Answered by Penny Nom. 





A convex quadrilateral in spherical geometry 
20080709 

From Joan: What is the min and max number of obtuse angles possible ia a convex quadrilateral in Spherical Geometry?
I know that the Saccheri has 2 obtuse angles and the Lambert has one, but are there other possibilities?
Thanks for your help. Answered by Chris Fisher. 





A rectangle 
20080626 

From SEBASTIAN: How to arrange quadrilateral in the form of a rectangle? Answered by Penny Nom. 





A quadrilateral 
20080508 

From reena: two exterior angles quadrilateral are 100 degrees 110 degrees each. two remaing interior one angle twice size other find size of each angle Answered by Penny Nom. 





Proving a quadrilateral is a rhombus 
20071203 

From Jeanie: How do you prove that a quadrilateral is a rhombus because the diagonals
of the quadrilateral are perpendicular and bisect each other using the 2column
proof method? Answered by Stephen La Rocque. 





Area of a quadrilateral 
20071010 

From Courtney: how would i find the area of a quadrilateral..
the sides are a (/) is 6cm, b (—) is 9 cm, and c (\) is 7 cm..
the angle between a and b is 140 degrees and b and c is 115 degrees.. Answered by Stephen La Rocque. 





A convex quadrilateral 
20070924 

From alex: if a convex quadrilateral ABCD is set up so that angles b and c are fixed (for example angle b= 73 and angle c =150), and
sides AB and CD are congruent; can angles a and b vary, or are they also fixed Answered by Brent Michelson. 





A quadrilateral problem 
20070829 

From James: The sides BC and AD of a quadrilateral ABCD are parallel. X is the midpoint of AB. The area of ABCD is Y. Find the area of the triangle CXD in the terms of Y. Answered by Harley Weston. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





The area of a quadrilateral 
20070610 

From Lucy: Calculate the area of the quadrilateral ABCD.
AB= 4.1cm, BC = 7.6cm, AD= 5.4 cm, CD= ?
Angle ABC = 117, Angle ADC = 62.
Give your answer correct to 3 significant figures. Answered by Stephen La Rocque and Penny Nom. 





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. 





A regular quadrilateral 
20070313 

From Jackie: How can the measure of each angle of a regular quadrilateral be determined? Answered by Haley Ess. 





Rectangles and squares 
20070131 

From Shelby: I am doing homework and I need to know why squares are rectangles but not all rectangles are squares? Answered by Penny Nom. 





A cyclic quadrilateral 
20061120 

From Namrata: If two sides of a cyclic quadrilateral are parallel, prove that (1) remaining two sides are equal, (2) both diagonals are equal. Answered by Penny Nom. 





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. 





The area of a quadrilateral 
20061031 

From Georgina: I would really like to know and be shown how to figure out the area of a quadrilateral. I already know that it is side x matching height but i need to be shown what to do. Could you please help? Answered by Penny Nom. 





A problem involving a quadrilateral 
20061013 

From Jeff: In the quadrilateral above, AB=AC=AD. If angle BCA = 65, then x=??? Answered by Penny Nom. 





The area of a quadrilateral 
20060914 

From A student: How can i find the area of a quadrilateral? Answered by Penny Nom. 





An irregular quadrilateral 
20060204 

From Christopher: Is there such a shape as an irregular quadrilateral with 4 equal sides? Answered by Penny Nom. 





Constructing a quadrilateral 
20051007 

From Jayasri:
Can we construct a unique quadrilateral with the following information:
The lenghts of all the sides of a quadrilateral are known.
The angle between one of the sides and the Xaxis is known.
Answered by Chris Fisher. 





Area of a region on a map 
20050428 

From Balachandar: Pl. find the attached map.
1. Can u pl. find out the total square are of WLMZ
2. Can u pl .find out the total square are of WXYZ  { A }
3. Can u pl .find out the total square are of XLMY  { B }
Pl .help me to find out the above.
..... Answered by Chris Fisher and Penny Nom. 





The area of a quadrilateral 
20050227 

From Jonathan: I want to know how to find the area of a quadrilateral. Answered by Penny Nom. 





Are the vetices of this quadrilateral concyclic? 
20050130 

From A student: Show that the peints A(2,0),B(6,6),C(1,7) and D(2,6) are concyclic. Also find its circum radius. Answered by Chris Fisher. 





The area of a quadrilateral 
20040825 

From Rich: I would like to know how to measure the area (the formula) of a quadrilateral. 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. 





How can you prove a quadrilateral to be a parallelogram? 
20010316 

From Joy: How can you prove a quadrilateral to be a parallelogram? Answered by Walter Whiteley. 





Area of a quadrilateral 
19991119 

From Zane Cram: I need the formula to calculate the area of an irregular sided rectangle. Each side has a different measurement or length. Answered by Walter Whiteley. 





A Kite 
19981007 

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

