Answer:
[tex]85.7 cm^2[/tex]
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:
[tex]A_T=\frac{1}{2}bh[/tex]
where
b = 6.8 cm is the base
h = 5.1 cm is the height
Substituting,
[tex]A_T=\frac{1}{2}(6.8)(5.1)=17.3 cm^2[/tex]
The area of the 3 rectangular faces is given by the product between the two sides, so:
[tex]A_1=(5.1 cm)(2.5 cm)=12.8 cm^2[/tex]
[tex]A_2=(8.5 cm)(2.5 cm)=21.3 cm^2[/tex]
[tex]A_3=(6.8 cm)(2.5 cm)=17 cm^2[/tex]
So the total area is:
[tex]A=2A_T+A_1+A_2+A_3=2(17.3)+12.8+21.3+17=85.7 cm^2[/tex]
