Area of Trapezoid

750+ wrote:

If BE || CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?

A. 12
B. 18
C. 24
D. 30
E. 48

Since BE and CD are parallel, the angles where BE and CD intersect AC are the same, and the angles where BE and CD intersect AD are the same.

Triangles BAE and CAD also share angle A.

Clearly since the three angles of triangle BAE are the same as the three angles of triangle CAD, BAE and CAD are similar triangles.

The lengths of corresponding sides of similar triangles are all in the same ratio.

So if BC = AB, then AC = 2AB and all the sides of CAD are twice the length of the corresponding sides of BAE.

Since AE = 4, AD = 8.

Since CD = 10, BE = 5

CA = 3 + 3 = 6

AD = 8

CD = 10

So CAD is a 6-8-10 (multiple of a 3-4-5) right triangle.

BA = 3

AD = 4

BD = 5

BAD is a 3-4-5 right triangle.

To find the area of a right triangle, you can simply multiply the lengths of the two perpendicular sides and divide by 2.

Area CAD = (6 x 8)/2 = 24

Area BAE = (3 x 4)/2 = 6

To get the area of the trapezoid, subtract area BAE from area CAD.

24 - 6 = 18

The correct answer is B.

750+ wrote:The right answer is B (18). Can someone please post a solution. Thanks

Consider the triangle ABE,
The two sides are 3 and 4. Hence the third side would be 5 (3 - 4 - 5 right triangle)
Area = 1/2 * 3 * 4 = 6

In triangle ABC,
The sides of this triangle are twice the sides of triangle ABE, hence area would be 2^2 times.
Area of ABC = 4*6 = 24

Area od the trapezoid = 24 - 6 = 18

Correct Option: B

Of course, there's also



So the trapezoid is (3/4) of the triangle, or (3/4) * 24.