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?
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.