Question

Find the lateral area and the surface area and round to the nearest whole number as needed.

Answer 1

- The lateral area is given by the formula:

`A=Perimeter* height`

Where:

Perimeter = 15 + 17 + side triangle

Height = 26 in26

First, we find the length of other side using the pythagoras theorem:

`\begin{gathered} a^2+b^2=c^2 \\ a^2+15^2=17^2 \\ a^2+225=289 \\ a^2+225-225=289-225 \\ a^2=64 \\ a^=√(64) \\ a=8 \end{gathered}`

Therefore the perimeter is:

`P=15+17+8=40\text{ in}`

And the lateral area is:

`A=40*26=1040\text{ in}^2`

- The surface area is given by

`A=lateal\text{ area+2\lparen area triangle\rparen}`

Then, the area of the triangle is:

`Atriangle=(bh)/(2)=(8*17)/(2)=(136)/(2)=68\text{ in}^2`

So, the surface area is:

`A=1040+2(68)=1040+136=1176\text{ in}^2`

Answer:

Lateral area = 1040 in^2

Surface area = 1176 in^2