Question

use formulas to find the lateral area and surface area of the prism
4in
5in
7in

Answer 1

To find the lateral area of a prism, we use the formula:

Lateral Area = perimeter of base * height

Since the base is a rectangle, the perimeter of the base is:

Perimeter = 2(length + width)
Perimeter = 2(5in + 7in)
Perimeter = 2(12in)
Perimeter = 24in

Now, we can find the lateral area:

Lateral Area = 24in * 4in
Lateral Area = 96 square inches

To find the surface area of the prism, we need to add the area of the two bases to the lateral area. Since the bases are rectangles, their area is:

Base Area = length * width
Base Area = 7in * 5in
Base Area = 35 square inches

Now, we can find the surface area:

Surface Area = 2(base area) + lateral area
Surface Area = 2(35in) + 96in
Surface Area = 70 square inches + 96 square inches
Surface Area = 166 square inches

Therefore, the lateral area of the prism is 96 square inches and the surface area is 166 square inches.