Answer:
89.44 square inches
Step-by-step explanation:
To find the surface area of a regular pyramid, you need to know the slant height, base length, and the height of the pyramid.
Given that the slant height (l) is 14 inches, the base length (b) is 5.2 inches, and the height (h) is 6 inches, we can calculate the surface area (A) using the formula:
A = (b * l) / 2 + b^2
First, let's calculate the lateral surface area. The lateral surface area is the sum of the areas of all the triangular faces of the pyramid.
To find the area of one triangular face, we use the formula: (base * height) / 2.
The base length (b) is 5.2 inches, and the height (h) is 6 inches. So, the area of one triangular face is (5.2 * 6) / 2 = 15.6 square inches.
Since a regular pyramid has a total of four triangular faces, the total lateral surface area is 4 * 15.6 = 62.4 square inches.
Next, let's calculate the area of the base. The base of a regular pyramid is a regular polygon, which means all sides are equal in length. To find the area of a regular polygon, we use the formula:
A = (n * s^2) / (4 * tan(π/n))
Where n is the number of sides and s is the length of one side.
In this case, the base is a square, so n = 4 and s = 5.2 inches.
Plugging these values into the formula, we get:
A = (4 * (5.2)^2) / (4 * tan(π/4))
Simplifying further:
A = (4 * 27.04) / (4 * 1) = 27.04 square inches
Finally, we can calculate the total surface area by summing the lateral surface area and the base area:
Total surface area = lateral surface area + base area
= 62.4 + 27.04
= 89.44 square inches
Therefore, the surface area of the regular pyramid is 89.44 square inches.
