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.

Front

What is the area of the base of a square pyramid if the side length is 4 meters?

Back

The area of the base (B) is calculated as B = side^2. For a side length of 4 meters, B = 4^2 = 16 square meters.

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.

Front

What is the slant height of a square pyramid?

Back

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

Front

If a square pyramid has a base side length of 5 meters and a slant height of 10 meters, what is its surface area?

Back

First, calculate the area of the base: B = 5^2 = 25 square meters. Then, calculate the perimeter: P = 4 * 5 = 20 meters. Finally, use the formula: SA = B + (1/2) * P * l = 25 + (1/2) * 20 * 10 = 25 + 100 = 125 square meters.

Front

What units are used to express the surface area of a square pyramid?

Back

Surface area is expressed in square units, such as square meters (m²), square centimeters (cm²), or square inches (in²).

Front

What is the relationship between the height and the slant height of a square pyramid?

Back

The height (h) and the slant height (l) of a square pyramid are related through the Pythagorean theorem: l² = h² + (side/2)².

Front

How does changing the base side length of a square pyramid affect its surface area?

Back

Increasing the base side length increases the area of the base and the perimeter, which in turn increases the surface area of the pyramid.

Front

What is the surface area of a square pyramid with a base area of 36 square feet and a slant height of 8 feet?

Back

First, calculate the perimeter: P = 4 * side length, where side length = sqrt(36) = 6 feet, so P = 4 * 6 = 24 feet. Then, use the formula: SA = B + (1/2) * P * l = 36 + (1/2) * 24 * 8 = 36 + 96 = 132 square feet.

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 surface area of the pyramid, which contributes to the total surface area.