Question

A triangular prism is covered with a foil label. The label does not cover the two ends. How much foil is necessary to cover the prism?

Answer 1

The area of the foil required to cover the triangular prism is 495 square feet

How to find the area of the foil

The area of the foil required is

• area of rectangular side

• area of rectangular base

Area of rectangular side

This side is 2.

= length * width + length * width

= 16.5 * 13 + 16.5 * 12

= 412.5 square ft

Area of rectangular base

= length * width

= 16.5 * 5

= 82.5 square ft

Area of foil is sum of the areas

= 412.5 + 82.5

= 495 square feet

Answer 2

The required foil is about 2l + lb sq units.

Explanation:

Given:

A triangular prism covered with foil.

To Find:

If two ends are not covered how much foil is required.

Solution:

The triangular prism has total of 5 faces as

two side faces ............... Rectangular shape

one bottom face.............rectangular shape

two side faces............ triangular face.

(Refer the attachment for diagram)

Area of triangle = 1/2(base × height)

Now there 2 traingles so

Total are for triangle = base × height

Area for bottom rectangle,

=length *breadth = l * b

Area for 2 side rectangles,

=2*(length * breadth)

=2*(l*S)

=2 * l * S

Hence required area =total area -area of triangle

(As triangles are presented at both ends) and as per condition.

= (2ls + lb + bh) - bh

= 2ls + lb.