What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
1. The area of the base:
Since the base is a square, we can use the formula for the area of a square: A = side^2.
The base edge is given as 1.5 cm, so the area of the base is 1.5^2 = 2.25 cm^2.
2. The area of the four triangular faces:
Each triangular face is a right triangle. We can use the formula for the area of a right triangle: A = 0.5 * base * height.
The base of each triangular face is the same as the base edge of the square pyramid, 1.5 cm.
The height of each triangular face is given as the slant height, which is 4 cm.
So, the area of each triangular face is 0.5 * 1.5 * 4 = 3.00 cm^2.
Since there are four triangular faces, the total area of the four faces is 4 * 3.00 = 12.00 cm^2.
Therefore, the surface area of the square pyramid is the sum of the base area and the area of the four faces:
Surface area = Base area + 4 * Face area
Surface area = 2.25 + 12.00 = 14.25 cm^2
Rounded to the nearest hundredth, the surface area is 14.25 cm^2.
To find the surface area of a square pyramid, we need to consider the area of the base and the lateral faces.
1. The area of the base:
- In a square pyramid, the base is a square.
- Since the base edge is given as 1.5 cm, we can use the formula for the area of a square: A = s^2, where s is the length of a side.
- Plugging in the value, we have A = (1.5 cm)^2 = 2.25 cm^2
2. The area of the lateral faces:
- In a square pyramid, there are 4 identical triangular lateral faces.
- To find the area of each triangular face, we can use the formula for the area of a triangle: A = (1/2)bh, where b is the base and h is the height.
- The base of each triangular face is the base edge, which is given as 1.5 cm.
- The height can be found using the Pythagorean theorem: h = sqrt(slant height^2 - (edge/2)^2) = sqrt(4 cm^2 - (1.5 cm/2)^2) = sqrt(16 cm^2 - 0.5625 cm^2) = sqrt(15.4375 cm^2) = 3.93 cm (rounded to the nearest hundredth).
- Plugging in the values, we have A = (1/2)(1.5 cm)(3.93 cm) = 2.945 cm^2
To find the total surface area, we can sum the area of the base and the area of the 4 lateral faces:
Total surface area = base area + lateral face area
= 2.25 cm^2 + 4(2.945 cm^2)
= 2.25 cm^2 + 11.78 cm^2
= 14.03 cm^2
Therefore, the surface area of the square pyramid is approximately 14.03 cm^2 (rounded to the nearest hundredth).