Surface Area of Pyramids Practice
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Question
Find the surface area of a rectangular pyramid with these measurements: l = 13 cm, w = 11 cm, and h = 8 cm. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
cm2
thats wrong bot
To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of each face, and then add them all together.
The area of the base can be found by multiplying the length (l) by the width (w):
Area of base = l * w = 13 cm * 11 cm = 143 cm²
Now, let's find the area of each face. Since a rectangular pyramid has 4 triangular faces, we need to find the area of each triangle.
The area of a triangle can be found using the formula:
Area of triangle = 1/2 * base * height
For our pyramid, the height (h) is given as 8 cm. Let's find the base of each triangle.
The base of each triangle is equal to the length or width of the base.
Let's find the area of the first face:
Base of triangle 1 = length of the base = 13 cm
Area of triangle 1 = 1/2 * base * height = 1/2 * 13 cm * 8 cm = 52 cm²
Now let's find the area of the other three faces. Since the base is a rectangle, the remaining two faces will have the same dimensions:
Base of triangle 2 = width of the base = 11 cm
Area of triangle 2 = 1/2 * base * height = 1/2 * 11 cm * 8 cm = 44 cm²
Area of triangle 3 = 44 cm²
Area of triangle 4 = 44 cm²
Now, let's add up the areas of all the faces:
Total surface area = Area of base + Area of triangle 1 + Area of triangle 2 + Area of triangle 3 + Area of triangle 4
Total surface area = 143 cm² + 52 cm² + 44 cm² + 44 cm² + 44 cm² = 327 cm²
Therefore, the surface area of the rectangular pyramid is 327 cm².