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:
[tex]\displaystyle A=\frac{b_1+b_2}{2}h[/tex]
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:
[tex]10^2=EC^2+BC^2[/tex]
The side BC can be found as half the difference of the bases:
[tex]BC=\frac{27-15}{2}=6[/tex]
Solving for EC:
[tex]EC^2=10^2-6^2=100-36=64[/tex]
[tex]EC=\sqrt{64}=8[/tex]
Now we have the height, calculate the area:
[tex]\displaystyle A=\frac{15+27}{2}*8[/tex]
[tex]\displaystyle A=\frac{42}{2}*8[/tex]
A = 168
The area of the trapezium is 168
