A quadrilateral with at least one pair of parallel sides is called a trapezium. Area of a trapezium is half of the product of sum of the parallel sides and height. Let's find its area as the sum of the area of a rectangle and a triangle.
Rectangle (ABCD) and right triangle (\triangle DCE) have the same area. They are joined to form a trapezoid, as shown. What is (DE)?
((A)12\qquad(B)13\qquad(C)14\qquad(D)15\qquad(E)16)
American Mathematical Contest 2014, AMC 8 Problem 14
Area of Trapezium
3 out of 10
Challenges and Thrills in Pre College Mathematics
Excursion Of Mathematics
Area of the triangle (\triangle DCE) = \frac{DC.CE}{2}
And the area of the square = (AB.AD)
It is given that (AB=5)
Then clearly (AB=DC=5)
(\frac{5.CE}{2}=30) , (30 is the area of the square)
This gives the value of (CE)
Now applying Pythagorean theorem in (\triangle ACE)
(DE^{2}=CE^{2}+DC^{2})
Which gives (DE=13)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.