Question

Find the surface area of the composite solid.

Answer 1

We have:

4 triangles with the base b = 5ft and the height h = 6ft

4 rectangles with the lenght l = 5ft and the width w = 4ft

1 square with side a = 5ft.

The formula of an area of a riangle:

$A_T=\dfrac{1}{2}bh$

Substitute:

$A_T=\dfrac{1}{2}(5)(6)=\dfrac{1}{2}(30)=15\ ft^2$

The formula of an area of a rectangle:

$A_R=lw$

Substitute:

$A_R=(5)(4)=20\ ft^2$

The formula of an area of a square:

$A_S=a^2$

Substitute:

$A_S=5^2=25\ ft^2$

The Surface Area of composite solid:

$SA=4A_T+4A_R+A_S$

Substitute:

$SA=4(15)+4(20)+25=60+80+25=165\ ft^2$

Answer: The Surface Area of the composite solid is 165 ft².