A square pyramid has base edges 10 in. long and a height of 4 in. Sketch the pyramid and find its surface area. Round your answer to the nearest tenth
To sketch the square pyramid, we need to draw a square for the base and then connect each corner of the base to a point directly above it. This point should be located at a distance equal to the height of the pyramid. Given that the base edges are 10 inches long and the height is 4 inches, we can proceed to draw the pyramid.
____________
/ \
/ \
/ \
/ \
A -------------- B
| |
| |
| |
C -------------- D
^
In the sketch above, A, B, C, and D represent the corners (or vertices) of the square base. The '^' symbol indicates the apex of the pyramid, located directly above the center of the square base.
To find the surface area of the square pyramid, we need to calculate the area of the square base and the areas of the four triangular faces.
1. Area of the square base:
The area of a square can be calculated using the formula: Area = side^2
Since the base edges are given as 10 inches, the area of the square base is:
Base Area = 10^2 = 100 square inches
2. Area of each triangular face:
The formula to calculate the area of a triangle is: Area = (1/2) × base × height
In this case, the base of each triangular face is the length of one side of the square base (10 inches), and the height is the slant height of the pyramid.
Using the Pythagorean theorem, we can find the slant height (l) of the pyramid:
l^2 = (1/2) × 10^2 + 4^2
l^2 = 50 + 16
l^2 = 66
l ≈ √66 ≈ 8.1 inches
The area of each triangular face is then calculated as:
Face Area = (1/2) × 10 × 8.1 = 40.5 square inches
3. Total surface area:
The total surface area of the pyramid is obtained by adding the areas of the square base and the four triangular faces:
Surface Area = Base Area + 4 × Face Area
Surface Area = 100 + 4 × 40.5 = 100 + 162 = 262 square inches
Therefore, the surface area of the square pyramid is approximately 262 square inches when rounded to the nearest tenth.