Question

What is the lateral surface area of the figure?

Answer 1

Answer:

$85.7 cm^2$

Step-by-step explanation:

The lateral surface of the figure is the sum of the areas of all the faces.

Here we have 5 faces:

- 2 identical right triangles

- 3 rectangular faces

The area of each triangular face is:

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

where

b = 6.8 cm is the base

h = 5.1 cm is the height

Substituting,

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

The area of the 3 rectangular faces is given by the product between the two sides, so:

$A_1=(5.1 cm)(2.5 cm)=12.8 cm^2$

$A_2=(8.5 cm)(2.5 cm)=21.3 cm^2$

$A_3=(6.8 cm)(2.5 cm)=17 cm^2$

So the total area is:

$A=2A_T+A_1+A_2+A_3=2(17.3)+12.8+21.3+17=85.7 cm^2$