Question

The longer diagonal of a right trapezoid is 13 cm. The longer base is 12 cm. Find the area of the trapezoid if the shorter base is 8 cm.

Answer 1

Draw a diagram of a right trapezoid .
B ---------------- C
.| ............ ............ *
.| ............ ............ ..... *
A --------------- -------------- D
Longer diagnal BD = 13cm
Longer base AD = 12cm
Shorter base BC = 8cm
Angle A is 90° , so △BAD is a right triangle .
AB^2 + AD^2 = BD^2
AB^2 + 12^2 = 13^2
AB^2 + 144 = 169
AB^2 = 25
AB = 5
So the area of trapezoid ABCD is (12+8)*5/2 = 50 [cm^2] .