The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find: Surface area of the pyramid
Usually the base is not included in finding the surface area of a pyramid, so wouldn't it just be
4(48) cm^2.
What am I missing?
48 times 4
To find the surface area of the pyramid, we need to calculate the area of the base and the sum of the areas of the lateral faces.
1. Start by calculating the area of the base:
- Since the base is a regular quadrilateral, it means it is a square.
- Let's assume the side length of the square base is 's'.
- The formula to calculate the area of a square is A = s^2, where A represents the area and s represents the length of a side.
- We are given that the area of the base is 36 cm^2. Therefore, we have: 36 = s^2.
- To find the value of 's', take the square root of both sides: sqrt(36) = sqrt(s^2).
- Simplifying, we get: 6 = s.
2. Calculate the area of one lateral face:
- A lateral face of a pyramid is a triangle.
- The formula to calculate the area of a triangle is A = (1/2) * base * height, where A represents the area, base represents the length of the base of the triangle, and height represents the perpendicular distance between the base and the apex.
- In this case, the base of the triangle is the same as the side length of the square base (s) and the height is not given.
- However, we can find the height using the Pythagorean theorem.
- Since the given lateral area is 48 cm^2, we have: 48 = (1/2) * s * height.
- Substitute the value of 's' which we found earlier (s = 6): 48 = (1/2) * 6 * height.
- Simplifying, we get: 48 = 3 * height.
- Divide both sides by 3 to isolate the height: 16 = height.
3. Calculate the total surface area:
- The total surface area of a pyramid is the sum of the area of the base and the areas of all the lateral faces.
- In this case, we have one base and four lateral faces.
- The area of the base is given as 36 cm^2.
- The area of each lateral face is given as 48 cm^2.
- Therefore, the total surface area is: 36 + (4 * 48) = 36 + 192 = 228 cm^2.
So, the surface area of the regular quadrilateral pyramid is 228 cm^2.