Question

Find the lateral area of the pyramid to the nearest whole unit.

A pyramid on its side is shown with its height measuring 22 m and its base measuring 8 m.
(1 point)
Responses

176 m2
176 m 2

352 m2
352 m 2

704 m2
704 m 2

416 m2

Answer 1

To find the lateral area of the pyramid, we need to calculate the surface area of the four triangular sides.

The formula for the lateral area of a pyramid is: 1/2 * perimeter of base * slant height

First, calculate the slant height of the pyramid using the Pythagorean theorem:

slant height = √(height^2 + (1/2 * base)^2)
slant height = √(22^2 + (1/2 * 8)^2)
slant height = √(484 + 16)
slant height = √500
slant height ≈ 22.36 m

Now, calculate the perimeter of the base:
perimeter of base = 4 * base
perimeter of base = 4 * 8
perimeter of base = 32 m

Finally, calculate the lateral area:
lateral area = 1/2 * 32m * 22.36m
lateral area = 16m * 22.36m
lateral area = 357.76 m^2

Therefore, the lateral area of the pyramid to the nearest whole unit is 358 m^2.

So, the closest option is 352 m2.