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
[tex]x=\frac{1}{2}(AD+BC)[/tex] ----> equation A
[tex]y=\frac{h}{2}[/tex] ----> [tex]h=2y[/tex] ----> equation B
Remember that
The area of rectangle is equal to
[tex]xy=10\ cm^2[/tex]
The area of trapezoid is equal to
[tex]A=\frac{1}{2}(AD+BC)h[/tex] -----> equation C
substitute equation A and equation B in equation C
[tex]A=(x)(2y)\\A=2xy[/tex]
The area of trapezoid is two times the area of rectangle
therefore
The area of trapezoid is 20 square centimeters
