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)).