Question

Which expression represents the total surface area, in square centimeters, of the square pyramid? A square pyramid. The square base has side lengths of 8.2 centimeters. The triangular sides have a height of 10.3 centimeters. (8.2) (8.2) + 4 (one-half (8.2) (10.3)) (8.2) (8.2) + 4 (one-half (8.2) (11.1)) (8.2) (10.3) + 2 (one-half (10.3) (10.3)) + 2 (one-half (8.2) (10.3)) (8.2) (10.3) + 2 (one-half (10.3) (11.1)) + 2 (one-half (8.2) (11.1))

Answer 1

Answer:

Step-by-step explanation:

If the base of the pyramid is squared,

Then, the area of the base is

A_b = s²

Where a is the side length

Given that the base has a side length of 8.2cm

Then,

A_b = 8.2² = (8.2)(8.2)

Now, the triangular side of the pyramid are identical and it has for sides,

We need to know the slant height,

Check attachment

using Pythagorean theorem

l² = h² + a²

l² = 10.3² + 4.1²

l² = 122.9

l = √122.9

l = 11.1 cm,

Now, to find the area of the four triangles

Area of a triangle is ½base × height

Now,

In the case of a pyramid the height is the slant height.

Four triangles will have an area of

A_t = 4 × ½ base × slant height

A_t = 4 × ½ × s× l

A_t = 4 (½)(8.2)(11.1)

A_t = 4(one-half (8.2)(11.1))

So, the total area is

A = A_b + A_t

A = (8.2)(8.2) + 4(one-half (8.2)(11.1))

Then, the first option is correct

Numerical value

A = (8.2)(8.2) + 4(one-half (8.2)(11.1))

A = 67.24 + 182.04

A = 249.28 cm²