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Snowcat [4.5K]
3 years ago
10

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

Mathematics
2 answers:
maw [93]3 years ago
5 0

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

anyanavicka [17]3 years ago
4 0
The answer is A) 70cm^2

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