Surface area of square pyramids

Front

What is the formula for the surface area of a square pyramid?

Back

The surface area (SA) of a square pyramid is given by the formula: SA = B + 1/2 * P * l, where B is the area of the base, P is the perimeter of the base, and l is the slant height.

Tags

CCSS.7.G.B.6

Front

What is the area of the base of a square pyramid with a side length of 4 inches?

Back

The area of the base (B) is calculated as B = side × side = 4 in × 4 in = 16 square inches.

Tags

CCSS.7.G.B.6

Front

How do you calculate the perimeter of the base of a square pyramid?

Back

The perimeter (P) of the base of a square pyramid is calculated as P = 4 × side length.

Tags

CCSS.3.MD.D.8

Front

If the side length of the base of a square pyramid is 5 meters, what is the perimeter of the base?

Back

The perimeter (P) is P = 4 × 5 m = 20 meters.

Tags

CCSS.3.MD.D.8

Front

What is the slant height of a square pyramid?

Back

The slant height (l) is the distance from the top vertex of the pyramid to the midpoint of one of the sides of the base.

Tags

CCSS.7.G.B.6

Front

How do you find the slant height of a square pyramid if the height is 6 inches and the base side length is 4 inches?

Back

Use the Pythagorean theorem: l = √(height² + (side/2)²) = √(6² + (4/2)²) = √(36 + 4) = √40 ≈ 6.32 inches.

Tags

CCSS.7.G.B.6

Front

What is the surface area of a square pyramid with a base side length of 8 inches and a slant height of 5 inches?

Back

First, calculate the base area: B = 8 in × 8 in = 64 in². Then, calculate the perimeter: P = 4 × 8 in = 32 in. Finally, SA = B + 1/2 * P * l = 64 in² + 1/2 * 32 in * 5 in = 64 in² + 80 in² = 144 in².

Tags

CCSS.7.G.B.6

Front

What is the surface area of a square pyramid with a base area of 25 m² and a slant height of 10 m?

Back

First, calculate the perimeter: P = 4 × √(25 m²) = 20 m. Then, SA = B + 1/2 * P * l = 25 m² + 1/2 * 20 m * 10 m = 25 m² + 100 m² = 125 m².

Tags

CCSS.7.G.B.6

Front

If a square pyramid has a surface area of 200 square yards and a base area of 100 square yards, what is the lateral surface area?

Back

The lateral surface area (LSA) is calculated as LSA = SA - B = 200 yd² - 100 yd² = 100 yd².

Tags

CCSS.7.G.B.6

Front

What is the lateral surface area of a square pyramid with a base side length of 6 inches and a slant height of 8 inches?

Back

First, calculate the perimeter: P = 4 × 6 in = 24 in. Then, LSA = 1/2 * P * l = 1/2 * 24 in * 8 in = 96 in².

Tags

CCSS.7.G.B.6