Describe the steps used to find the lateral area of a square pyramid given its height and base measurements.
To find the lateral area of a square pyramid, follow these steps:
Step 1: Determine the base perimeter
- Since a square pyramid has a square base, you need to find the perimeter of the base.
- The perimeter of a square is calculated by multiplying one side by 4, as all four sides of a square are equal in length.
- So, multiply the length of one side of the square base by 4 to find the base perimeter.
Step 2: Calculate the slant height
- The slant height is the height of each triangular face on the pyramid.
- To calculate the slant height, use the Pythagorean theorem.
- The Pythagorean theorem states that the square of the hypotenuse (slant height) of a right triangle is equal to the sum of the squares of the other two sides (base height and half the base length).
- So, use the height of the pyramid and half the length of one side of the base to find the slant height using the Pythagorean theorem.
Step 3: Calculate the lateral area
- The lateral area of a pyramid is the sum of the areas of all the triangular faces.
- The area of a triangle can be calculated using the formula: Area = (1/2) * base * height.
- In this case, the base is the length of one side of the square base, and the height is the slant height.
- Multiply the base length by the slant height and divide it by 2 to get the area of one triangular face.
- Since there are four triangular faces, multiply the area of one triangular face by 4 to get the total lateral area of the square pyramid.
By following these steps, you can find the lateral area of a square pyramid given its height and base measurements.