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

(A)
`70cm^2`

Explanation:

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

`(PT)/(ST)=tan45^(\circ)`

⇒
`(5)/(ST)=1`

⇒
`ST=5cm`

Now, area ΔPST=
`(1)/(2){*}5{*}5=(25)/(2)cm^2`

Also, area ΔQUR=
`(1)/(2){*}5{*}3=(15)/(2)cm^2`

Area rectangle PQUT=
`l{*}b=10{*}5=50cm^2`

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

=
`(25)/(2)+(15)/(2)+50`

=
`70cm^2`

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