Question

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

1/2*h(b1+b2)) *
E
15
А
10
M.
B
Q
27
RI
1

Answer 1

The area of the trapezium is 168

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=(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=(27-15)/(2)=6`

Solving for EC:

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

`EC=√(64)=8`

Now we have the height, calculate the area:

`\displaystyle A=(15+27)/(2)*8`

`\displaystyle A=(42)/(2)*8`

A = 168

The area of the trapezium is 168