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 4m?

Back

The area of the base (B) is calculated as B = side². For a side length of 4m, B = 4m * 4m = 16m².

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 5m, what is the perimeter?

Back

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

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 if the height of the pyramid is 6m and the base side length is 4m?

Back

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

Tags

CCSS.7.G.B.6

Front

What is the total surface area of a square pyramid with a base side of 4m and a slant height of 5m?

Back

First, calculate the base area: B = 16m². Then, calculate the lateral area: LA = 1/2 * P * l = 1/2 * 16m * 5m = 40m². Total surface area = B + LA = 16m² + 40m² = 56m².

Tags

CCSS.7.G.B.6

Front

If a square pyramid has a base area of 25cm² and a lateral area of 60cm², what is its total surface area?

Back

Total surface area = base area + lateral area = 25cm² + 60cm² = 85cm².

Tags

CCSS.7.G.B.6

Front

What is the surface area of a square pyramid with a base side of 6m and a slant height of 7m?

Back

Base area = 6m * 6m = 36m². Perimeter = 4 * 6m = 24m. Lateral area = 1/2 * 24m * 7m = 84m². Total surface area = 36m² + 84m² = 120m².

Tags

CCSS.7.G.B.6

Front

What is the significance of the slant height in calculating the surface area of a square pyramid?

Back

The slant height is crucial for calculating the lateral area, which contributes to the total surface area of the pyramid.

Tags

CCSS.7.G.B.6