To find the surface area of a rectangular pyramid, we first need to find the area of the base, and then add the area of each triangular face.
The area of the base of the pyramid is found by multiplying the length (l) by the width (w):
Base area = l × w = 13 cm × 11 cm = 143 cm²
The surface area of each triangular face is found by multiplying half the base width, or the length (l) of the base, by the slant height (s), and then dividing by 2:
Surface area of each triangular face = (l × s) / 2
To find the slant height, we use the Pythagorean theorem: s² = l² + h²
s² = 13² + 8² = 169 + 64 = 233
s ≈ √233 ≈ 15.26 cm
Therefore, the surface area of each triangular face is approximately (13 cm × 15.26 cm) / 2 ≈ 99.89 cm².
Since there are four triangular faces, the total surface area of the pyramid is:
Total surface area = Base area + 4 × Surface area of each triangular face
Total surface area ≈ 143 cm² + 4 × 99.89 cm² = 143 cm² + 399.56 cm² ≈ 542.56 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is approximately 542.56 cm².
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)
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Apologies for the mistake. Let's try again.
The surface area of a rectangular pyramid is given by the formula:
Surface area = Base area + (0.5 × perimeter of base × slant height)
First, let's find the base area by multiplying the length (l) and width (w) of the base:
Base area = l × w = 13 cm × 11 cm = 143 cm²
Next, let's find the perimeter of the base. Since it's a rectangular base, we can use the formula:
Perimeter = 2(l + w) = 2(13 cm + 11 cm) = 2(24 cm) = 48 cm
Now, let's find the slant height (s) using the Pythagorean theorem:
s² = l² + h²
s² = 13² + 8²
s² = 169 + 64
s² = 233
s ≈ √233 ≈ 15.26 cm
Finally, we can substitute the values into the formula to find the surface area:
Surface area = 143 cm² + (0.5 × 48 cm × 15.26 cm)
Surface area = 143 cm² + (0.5 × 729.48 cm²)
Surface area = 143 cm² + 364.74 cm²
Surface area ≈ 507.74 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is approximately 507.74 cm².
The surface area of a rectangular pyramid is given by the formula:
Surface area = Base area + (0.5 × perimeter of base × slant height)
First, let's find the base area by multiplying the length (l) and width (w) of the base:
Base area = l × w = 13 cm × 11 cm = 143 cm²
Next, let's find the perimeter of the base. Since it's a rectangular base, we can use the formula:
Perimeter = 2(l + w) = 2(13 cm + 11 cm) = 2(24 cm) = 48 cm
Now, let's find the slant height (s) using the Pythagorean theorem:
s² = l² + h²
s² = 13² + 8²
s² = 169 + 64
s² = 233
s ≈ √233 ≈ 15.26 cm
Finally, we can substitute the values into the formula to find the surface area:
Surface area = 143 cm² + (0.5 × 48 cm × 15.26 cm)
Surface area = 143 cm² + (0.5 × 729.48 cm²)
Surface area = 143 cm² + 364.74 cm²
Surface area ≈ 507.74 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is approximately 507.74 cm².
Restart it and get a new answer.
Apologies for the confusion. Let's start over and find the correct answer.
To find the surface area of a rectangular pyramid, we need to find the area of the base and the lateral area.
The base area of the pyramid is given by the formula:
Base area = l × w
In this case, the length (l) is 13 cm and the width (w) is 11 cm, so:
Base area = 13 cm × 11 cm = 143 cm²
Next, we need to find the lateral area of the pyramid. This is the sum of the areas of the four triangular faces. Each triangular face has a base equal to the length of the base (l) and a height equal to the slant height (s).
To find the slant height (s), we will use the Pythagorean theorem. The slant height (s) is the hypotenuse of a right triangle formed by the height (h), the length of the base (l), and the slant height (s).
Using the Pythagorean theorem:
s² = l² + h²
s² = 13² + 8²
s² = 169 + 64
s² = 233
s ≈ √233 ≈ 15.26 cm
Now that we have the slant height, we can calculate the lateral area of each triangular face using the formula:
Lateral area of each triangular face = (0.5 × l × s)
In this case, the length of the base (l) is 13 cm, and the slant height (s) is approximately 15.26 cm:
Lateral area of each triangular face = (0.5 × 13 cm × 15.26 cm) = 98.99 cm²
Since there are four triangular faces, the total lateral area is:
Total lateral area = 4 × Lateral area of each triangular face = 4 × 98.99 cm² = 395.96 cm²
Finally, we can calculate the surface area by adding the base area and the total lateral area:
Surface area = Base area + Total lateral area = 143 cm² + 395.96 cm² = 538.96 cm²
Therefore, the surface area of the rectangular pyramid is 538.96 cm² rounded to the nearest hundredth.
To find the surface area of a rectangular pyramid, we need to find the area of the base and the lateral area.
The base area of the pyramid is given by the formula:
Base area = l × w
In this case, the length (l) is 13 cm and the width (w) is 11 cm, so:
Base area = 13 cm × 11 cm = 143 cm²
Next, we need to find the lateral area of the pyramid. This is the sum of the areas of the four triangular faces. Each triangular face has a base equal to the length of the base (l) and a height equal to the slant height (s).
To find the slant height (s), we will use the Pythagorean theorem. The slant height (s) is the hypotenuse of a right triangle formed by the height (h), the length of the base (l), and the slant height (s).
Using the Pythagorean theorem:
s² = l² + h²
s² = 13² + 8²
s² = 169 + 64
s² = 233
s ≈ √233 ≈ 15.26 cm
Now that we have the slant height, we can calculate the lateral area of each triangular face using the formula:
Lateral area of each triangular face = (0.5 × l × s)
In this case, the length of the base (l) is 13 cm, and the slant height (s) is approximately 15.26 cm:
Lateral area of each triangular face = (0.5 × 13 cm × 15.26 cm) = 98.99 cm²
Since there are four triangular faces, the total lateral area is:
Total lateral area = 4 × Lateral area of each triangular face = 4 × 98.99 cm² = 395.96 cm²
Finally, we can calculate the surface area by adding the base area and the total lateral area:
Surface area = Base area + Total lateral area = 143 cm² + 395.96 cm² = 538.96 cm²
Therefore, the surface area of the rectangular pyramid is 538.96 cm² rounded to the nearest hundredth.