Asher will need c. 936 cm² of paint to cover both the bookends.
Step-by-step 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 = [tex]\frac{1}{2} (9)(12) = 54[/tex] cm².
Area of both triangles = 2× Area of 1 triangle [tex]= 2(54)[/tex] = 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 [tex]= (10)(15) = 150[/tex] cm².
Area of a rectangle with width 9 cm [tex]= (10)(9) = 90[/tex] cm².
Area of a rectangle with width 12 cm [tex]= (10)(12) = 120[/tex] cm².
Step 4:
The area of the entire triangular prism = Area of 2 triangles + Area of all the 3 rectangles = [tex]108+150+90+120 = 468[/tex] cm².
This is the surface area of 1 bookend. As both the bookends are similar.
The surface area of 2 bookends [tex]= 2(468) = 936[/tex] cm².
Asher will need 936 cm² of paint to cover both the bookends.
