Answer:
101.9 sq ft
Step-by-step explanation:
The figure is missing: find it in attachment.
Here we want to find the lateral surface area of the figure, which is the sum of the areas of all faces.
We have in total 5 faces:
- 1 of them is rectangle with sizes (8.5 ft x 3.3 ft), so its area is
[tex]A_1=8.5 \cdot 3.3 =28.1 ft^2[/tex]
- 1 of them is a rectangle with sizes (3.3 ft x 5.1 ft), so its area is
[tex]A_2 = 3.3\cdot 5.1 =16.8 ft^2[/tex]
- 1 of them is a rectangle with sizes (6.8 ft x 3.3 ft), so its area is
[tex]A_3 = 6.8\cdot 3.3 =22.4 ft^2[/tex]
- Finally, we have 2 triangular faces (top and bottom), so their area is
[tex]A_T=\frac{1}{2}bh[/tex]
where
b = 5.1 ft is the base
h = 6.8 ft is the height (because the triangle is a right triangle)
So the area of the triangle is
[tex]A_T=\frac{1}{2}(5.1)(6.8)=17.3 ft^2[/tex]
So the total lateral surface area of the figure is:
[tex]A=A_1+A_2+A_3+2A_T=28.1+16.8+22.4+2(17.3)=101.9 ft^2[/tex]
