How to find the surface area of a pyramid - SAT Math

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Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

Question

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Answer

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Compare your answer with the correct one above

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