Question
Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.
Note: The opposite triangles are congruent.
Note: Figure is not drawn to scale.
If a measures 8 cm, b measures 4 cm, and d measures 9 cm, what is the surface area of the rectangular pyramid?
Note: The opposite triangles are congruent.
Note: Figure is not drawn to scale.
If a measures 8 cm, b measures 4 cm, and d measures 9 cm, what is the surface area of the rectangular pyramid?
Answers
GPT 3.5
To find the surface area of the rectangular pyramid, we need to find the area of each of the 5 faces and then add them together.
1. Base of the pyramid (rectangular shape):
The area of the base = a * b = 8 cm * 4 cm = 32 cm^2
2. Four triangular faces:
Each triangular face is a right triangle with legs a and d, and hypotenuse b. The area of each triangular face can be found using the formula for the area of a triangle: 1/2 * base * height.
The base of each triangle (a) = 8 cm
The height of each triangle (d) = 9 cm
The area of each triangle = 1/2 * a * d = 1/2 * 8 cm * 9 cm = 36 cm^2
Since there are 4 triangular faces, the total area of all four triangular faces = 4 * 36 cm^2 = 144 cm^2
3. Adding up the areas of all faces:
Total surface area = base area + area of all four triangular faces
Total surface area = 32 cm^2 + 144 cm^2 = 176 cm^2
Therefore, the surface area of the rectangular pyramid is 176 square centimeters.
1. Base of the pyramid (rectangular shape):
The area of the base = a * b = 8 cm * 4 cm = 32 cm^2
2. Four triangular faces:
Each triangular face is a right triangle with legs a and d, and hypotenuse b. The area of each triangular face can be found using the formula for the area of a triangle: 1/2 * base * height.
The base of each triangle (a) = 8 cm
The height of each triangle (d) = 9 cm
The area of each triangle = 1/2 * a * d = 1/2 * 8 cm * 9 cm = 36 cm^2
Since there are 4 triangular faces, the total area of all four triangular faces = 4 * 36 cm^2 = 144 cm^2
3. Adding up the areas of all faces:
Total surface area = base area + area of all four triangular faces
Total surface area = 32 cm^2 + 144 cm^2 = 176 cm^2
Therefore, the surface area of the rectangular pyramid is 176 square centimeters.