math problem

Question

What is the area of an isosceles trapezoid if the length of its shorter base is 18 cm, the length of an altitude is 9 cm, and the measure of the acute angle is 45º.

What is the area of an isosceles trapezoid if the length of its shorter base is 18 cm, the length of an altitude is 9 cm, and the measure of the acute angle is 45º.

Answer 1

Hi Patricia,

 

The area of a trapezoid, A = [(shorter base + longer base)*altitude] / 2

 

If the acute angle is 45 deg, then the other side of the right triangle formed by drawing altitudes from the two vertices of the shorter base to the longer base will also be equal to altitude. There will be two isosceles right triangles and they are congruent.

Then, the longer base will be 9+9+18 = 36 cm

 

A = ((36+18)*9) / 2 = 243 cm^2