Question

Help? It says find the surface area of the triangular prism, and the base is an isosceles triangle

Answer 1

Given:

The figure and dimensions of the triangular prism.

The base is an isosceles triangle

To find:

The area of the triangular prism.

Solution:

The area of a triangle is:

`A_1=(1)/(2)* base* height`

The base of the triangle is 24 cm and the height is 35 cm. So, the area of a triangular base (in sq. cm) is:

`A_1=(1)/(2)* 24* 35`

`A_1=12* 35`

`A_1=420`

The bases of the triangular prism are same. So, the area of the other triangular base is
`A_2=420` sq. cm.

The sides of the base triangle are 37 cm, 37 cm and 24 cm. So, the perimeter of the base triangle is:

`P=37+37+24`

`P=98`

Now, the curved surface area of the prism is:

`A_3=P* h`

Where, P is the base perimeter and h is the height of the prism.

The base perimeter of the triangular prism is 98 cm and the height is 48 cm. So, the curved surface area is:

`A_3=98* 48`

`A_3=4704`

Now, the total area of the triangular prism is:

`A=A_1+A_2+A_3`

`A=420+420+4704`

`A=5544`

Therefore, the area of the given triangular prism is 5544 sq. cm.