Question

Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale.
(picture attached below)

Answer Choices:
A. 70 cm²
B. 50 cm²
C. 75 cm²
D. 65 cm²

thank you so much in advance! :)

Answer 1

The answer is A) 70cm^2

Answer 2

Answer:

(A)$70cm^2$

Step-by-step explanation:

Given is the trapezoid which consists of two triangles and one rectangle, thus from ΔPST, we have

$\frac{PT}{ST}=tan45^{\circ}$

⇒$\frac{5}{ST}=1$

⇒$ST=5cm$

Now, area ΔPST=$\frac{1}{2}{\times}5{\times}5=\frac{25}{2}cm^2$

Also, area ΔQUR=$\frac{1}{2}{\times}5{\times}3=\frac{15}{2}cm^2$

Area rectangle PQUT=$l{\times}b=10{\times}5=50cm^2$

Therefore, area trapezoid PQRS= area ΔPST+area ΔQUR+Area rectangle PQUT

=$\frac{25}{2}+\frac{15}{2}+50$

=$70cm^2$

Hence, area of trapezoid= $70cm^2$