Question

PICTURE BELOW Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?

A) 2
B) 3
C) 4
D) 5

Answer 1

The carpenter will need 2 plywood to build the prism.

Explanation:

Given:

The size of the plywood = 4 ft x 8 ft

1 Unit = 4 feet

To Find :

Number of plywood sheets the carpenter would need = "

Solution:

Step 1: Find the area of square

Area of the square is

=>
`4^2`

=>
`16 cm^2`

Here we have 3 square, so

`3 * 16`

=>
`48 ft^2`

Step 2 : Area of the triangle

Area of the triangle is

=>
`(1)/(2) * b* h`

=>
`(1)/(2) * 4 * 4`

=>
`(16)/(2)`

=>
`8ft^2`

`2 * 8 = 16ft^2`

Step 3: Finding the plywood needed

the total area of the triangular prism is

48 + 16=
`64 ft^2`

Area of the plywood wood is

=>
`4 * 8`

=>
`32 ft^2`

Number of plywood required =
`\frac{\text {area of the prism}}{\text{area of one plywood}}`

=>
`(64)/(32)`

=> 2