Question

29. Find the height of the trapezoid. Use this height to find the area. (A =

Answer 1

Answer:

The area of the trapezium is 168

Step-by-step explanation:

Area of a Trapezoid

Given a trapezoid of parallel bases b1 and b2, and height h, the area is calculated with the formula:

$\displaystyle A=\frac{b_1+b_2}{2}h$

The trapezoid in the figure has b1=15 and b2=27. We need to find the height. If we focus on triangle BCD, we can calculate the height as the distance EC by using the Pythagora's Theorem:

$10^2=EC^2+BC^2$

The side BC can be found as half the difference of the bases:

$BC=\frac{27-15}{2}=6$

Solving for EC:

$EC^2=10^2-6^2=100-36=64$

$EC=\sqrt{64}=8$

Now we have the height, calculate the area:

$\displaystyle A=\frac{15+27}{2}*8$

$\displaystyle A=\frac{42}{2}*8$

A = 168

The area of the trapezium is 168