Question

Two identical square pyramids were joined at their bases to form the composite figure below.

Which expression represents the total surface area, in square centimeters, of the figure?​

Answer 1

The expression that represents the total surface area, in square centimeters, of the composite figure is (24) (24) + 8 (one-half (24) (5)) + 8 (one-half (24) (13)).

The total surface area of the composite figure is the sum of the surface areas of the two square pyramids and the rectangle that forms the base.

The surface area of a pyramid is the sum of the areas of its base and four lateral faces. The lateral faces of a square pyramid are triangles, so the surface area of a square pyramid is calculated as follows:

Surface area of a square pyramid = Area of the base + 4 * Area of a lateral face

The area of the base of a square pyramid is the area of a square. The area of a square is calculated as follows:

Area of a square = side^2

The area of a lateral face of a square pyramid is the area of a triangle. The area of a triangle is calculated as follows:

Area of a triangle = 1/2 * base * height

In the composite figure, each square pyramid has a base side length of 24 centimeters and a height of 5 centimeters. Therefore, the surface area of each square pyramid is calculated as follows:

Surface area of each square pyramid = Area of the base + 4 * Area of a lateral face

Surface area of each square pyramid = 24^2 + 4 * 1/2 * 24 * 5

Surface area of each square pyramid = 576 + 240

Surface area of each square pyramid = 816 square centimeters

The rectangle that forms the base of the composite figure has dimensions of 24 centimeters by 48 centimeters. Therefore, the area of the rectangle is calculated as follows:

Area of the rectangle = 24 * 48

Area of the rectangle = 1152 square centimeters

The total surface area of the composite figure is the sum of the surface areas of the two square pyramids and the rectangle that forms the base. Therefore, the total surface area of the composite figure is calculated as follows:

Total surface area of the composite figure = 2 * Surface area of each square pyramid + Area of the rectangle

Total surface area of the composite figure = 2 * 816 + 1152

Total surface area of the composite figure = 1632 + 1152

Total surface area of the composite figure = 2784 square centimeters

Therefore, the expression that represents the total surface area, in square centimeters, of the composite figure is (24) (24) + 8 (one-half (24) (5)) + 8 (one-half (24) (13)).

Question

Two identical square pyramids were joined at their bases to form the composite figure below. 2 square pyramids have a base of 24 centimeters by 24 centimeters. The triangular sides have a height of 5 centimeters. [Not drawn to scale] Which expression represents the total surface area, in square centimeters, of the figure? 8 (one-half (24) (5)) 8 (one-half (24) (13)) (24) (24) + 8 (one-half (24) (5)) (24) (24) + 8 (one-half (24) (13)).

Answer 2

Explanation:

The given options are

A. 8 (one-half (24) (5))

B. 8 (one-half (24) (13))

C. (24) (24) + 8 (one-half (24) (5))

D. (24) (24) + 8 (one-half (24) (13))

We, should know that, the base area is covered and it cannot be seen, so the shape does not have a physical base area.

Then,

We need to find the area of the 8 sides triangle that formed the pyramid

Area of a triangle is ½base × height

But for a pyramid the height is the slant height

Then, the eight triangles are identical

Then, the area of the eight triangles is

A = 8 × ½ base × slant height

From the diagram,

The base length is 24cm

And the slant height is 13cm

Then,

A = 8 × ½ b × l

A = 8 × one-half × 24 × 13

A = 8(one-half)(24)(13) cm²

So, the correct answer is B

Numeral value

A = 8 × ½ × 24 × 13

A = 1248 cm²