Answer:
Explanation:
To find the surface area of a square pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.
The area of the base of the pyramid is:
Area of square base = (base length)^2
Area of square base = 3^2
Area of square base = 9 square inches
To find the area of each triangular face, we need to first find the length of each side. Since the base is a square, all sides are equal to 3 inches. The slant height is given as 7 inches, which is the height of each triangular face.
Using the Pythagorean theorem, we can find the length of each side of the triangular face:
(side length)^2 + (height)^2 = (slant height)^2
(side length)^2 + 7^2 = 7^2
(side length)^2 = 7^2 - 7^2
(side length)^2 = 24.5
side length ≈ 4.95
The area of each triangular face is:
Area of triangular face = (1/2) × (base length) × (height)
Area of triangular face = (1/2) × 3 × 7
Area of triangular face = 10.5 square inches
Therefore, the total surface area of the square pyramid is:
Total surface area = Area of base + Sum of areas of four triangular faces
Total surface area = 9 + 4(10.5)
Total surface area = 42 square inches
Hence, the surface area of this square pyramid is 42 square inches.