Surface Area of Square Based Pyramids

Front

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

Back

Surface Area = 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 does 'B' represent in the context of a square-based pyramid?

Back

'B' represents the area of the base of the pyramid.

Front

How do you calculate the area of the base (B) of a square-based pyramid?

Back

Area of the base (B) = side length × side length.

Front

What is the perimeter (P) of the base of a square-based pyramid?

Back

Perimeter (P) = 4 × side length.

Front

What is the slant height of a pyramid?

Back

The slant height is the distance from the apex of the pyramid to the midpoint of a side of the base.

Front

If the side length of the base of a square-based pyramid is 4, what is the area of the base (B)?

Back

B = 4 × 4 = 16.

Front

If the side length of the base of a square-based pyramid is 4, what is the perimeter (P)?

Back

P = 4 × 4 = 16.

Front

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

Back

The slant height, height, and half the base length form a right triangle.

Front

If the slant height of a pyramid is 10 and the base length is 8, what is the height of the pyramid?

Back

Using the Pythagorean theorem: height = √(slant height² - (base length/2)²) = √(10² - 4²) = √(100 - 16) = √84 ≈ 9.17.

Front

What is the total surface area of a square-based pyramid with a base area of 16 and a slant height of 10?

Back

Total Surface Area = 16 + 1/2 * 16 * 10 = 16 + 80 = 96.