Question

Please help to find the area of this trapezium

Answer 1

Answer:

The area of trapezoid is 20 square centimeters

Step-by-step explanation:

Let

x -----> the length of rectangle

y ----> the height of rectangle

h ----> height of trapezoid

Applying the Trapezoid Mid-segment Theorem we have that

$x=\frac{1}{2}(AD+BC)$ ----> equation A

$y=\frac{h}{2}$ ----> $h=2y$ ----> equation B

Remember that

The area of rectangle is equal to

$xy=10\ cm^2$

The area of trapezoid is equal to

$A=\frac{1}{2}(AD+BC)h$ -----> equation C

substitute equation A and equation B in equation C

$A=(x)(2y)\\A=2xy$

The area of trapezoid is two times the area of rectangle

therefore

The area of trapezoid is 20 square centimeters