Question

I need help lol. Find the lateral surface area of the figure to the nearest tenth.

Answer 1

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

$A_1=8.5 \cdot 3.3 =28.1 ft^2$

- 1 of them is a rectangle with sizes (3.3 ft x 5.1 ft), so its area is

$A_2 = 3.3\cdot 5.1 =16.8 ft^2$

- 1 of them is a rectangle with sizes (6.8 ft x 3.3 ft), so its area is

$A_3 = 6.8\cdot 3.3 =22.4 ft^2$

- Finally, we have 2 triangular faces (top and bottom), so their area is

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

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

$A_T=\frac{1}{2}(5.1)(6.8)=17.3 ft^2$

So the total lateral surface area of the figure is:

$A=A_1+A_2+A_3+2A_T=28.1+16.8+22.4+2(17.3)=101.9 ft^2$