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MariettaO [177]
3 years ago
11

Find the surface area of the following figure

Mathematics
1 answer:
Julli [10]3 years ago
3 0

Answer:

<h2>510.4 ft²</h2>

Step-by-step explanation:

We have:

two trapezoids with bases 15ft and 7ft and height 5ft.

four rectangles 5ft × 11ft, 15ft × 11ft, 9.4ft × 11ft and 7ft × 11ft.

The formula of an area of a trapezoid:

A_t=\dfrac{b_1+b_2}{2}\cdot h

b₁, b₂ - bases

h - height

Substitute:

A_t=\dfrac{15+7}{2}\cdot5=\dfrac{22}{2}\cdot5=(11)(5)=55\ ft^2

The formula of an area of a rectangle:

A_r=lw

l - length

w - width

The dimensions of rectangle l × w

Subtitute:

A_1=(5)(11)=55\ ft^2\\\\A_2=(15)(11)=165\ ft^2\\\\A_3=(9.4)(11)=103.4\ ft^2\\\\A_4=(7)(11)=77\ ft^2

The surface area of the figure:

[tex]S.A.=2A_t+A_1+A_2+A_3+A_4\\\\S.A.=2(55)+55+165+103.4+77=510.4\ ft^2[/text]

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