Answer:
A=42 ft²
Step-by-step explanation:
The area of the trapezoid is given by the formula
[tex]Area= \frac{1}{2} (sum \: of \: bases) \times h[/tex]
The bases are 9ft, and (9+3=12) ft.
To find the height of the trapezoid, we use the Pythagoras Theorem,
[tex] {h}^{2} + {3}^{2} = {5}^{2} [/tex]
Evaluate the exponents:
[tex] {h}^{2} + 9 = 25[/tex]
[tex] {h}^{2} = 25 - 9[/tex]
[tex] {h}^{2} = 16[/tex]
Take square root:
[tex]h = \sqrt{16} = 4ft[/tex]
The area of the trapezoid is:
[tex] = \frac{1}{2} (12 + 9) \times 4[/tex]
[tex] = 2 \times 21[/tex]
[tex] = 42 {ft}^{2} [/tex]
