SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Surface Area of Pyramid

Grade: 4-a Lesson: S3-L6

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Find the surface area of the triangular pyramid.

Step 1a

Given that the base area(B) is 81 square inches and the slant height(l) is 12 inches.

The formula gives the surface area of a triangular pyramid: SA = \$"B" + 1/2 "pl"\$

$1a$

Explanation: In this step, explaining the provided values, the Base area is 81 in², and the slant height is 12 in. The formula for triangular pyramid surface area: \$"SA" = "B" + 1/2"pl"\$.

Step 1b

The perimeter of the base is the sum of the lengths of the three sides of the base triangle. Since each side is 10 in, the perimeter is 10 + 10 + 10 = 30 in.

Explanation: In this step, find the base perimeter by adding the lengths of the three sides, each 10 inches, for a total of 30 inches.

Step 1c

Plug these values into the formula and simplify: SA = \$81 + 1/2(30)(12)\$

SA = \$81 + 180\$

SA = \$261 "in"^2\$

Therefore, the surface area of the triangular pyramid is \$261 "in"^2\$.

Explanation: In this step, calculate the surface area of the triangular pyramid by substituting values into the formula and simplifying, resulting in 261 in².