Question

Asher built two bookends and wants to paint them. How much paint will he need to cover the surface of both bookends? 468 cm2 576 cm2 936 cm2 1,044 cm2

Answer 1

c

Explanation:

Answer 2

Asher will need c. 936 cm² of paint to cover both the bookends.

Explanation:

Step 1:

To determine the amount of paint needed, we determine the surface area of the triangular prisms.

To calculate the triangular prism's surface area, we calculate the areas of all the 5 sides. We divide the prism into 2 triangles and 3 rectangles, find the areas individually and then sum them all up in order to determine the area of the entire triangular prism.

Step 2:

There are two triangles with base lengths of 9 cm and heights of 12 cm. A triangle's area is half the product of the base length and its height.

Area of 1 triangle =
`(1)/(2) (9)(12) = 54` cm².

Area of both triangles = 2× Area of 1 triangle
`= 2(54)` = 108 cm².

Step 3:

There are three rectangles with a common length of 10 cm but there are three different widths. Any rectangle's area is calculated by multiplying the rectangle's length with its width.

Area of a rectangle with width 15 cm
`= (10)(15) = 150` cm².

Area of a rectangle with width 9 cm
`= (10)(9) = 90` cm².

Area of a rectangle with width 12 cm
`= (10)(12) = 120` cm².

Step 4:

The area of the entire triangular prism = Area of 2 triangles + Area of all the 3 rectangles =
`108+150+90+120 = 468` cm².

This is the surface area of 1 bookend. As both the bookends are similar.

The surface area of 2 bookends
`= 2(468) = 936` cm².

Asher will need 936 cm² of paint to cover both the bookends.