Question

what is the surface area of this rectangular pyramid? 5 m 5 m 9 m square meters submit

Explanation:

Step1: Identify the base and lateral faces

The base is a square with side length \( 5 \, \text{m} \), and there are four triangular lateral faces. Each triangular face has a base of \( 5 \, \text{m} \) and a slant height of \( 9 \, \text{m} \).

Step2: Calculate the area of the base

The area of the square base is \( \text{side}^2 \), so:
\( \text{Base Area} = 5 \times 5 = 25 \, \text{m}^2 \)

Step3: Calculate the area of one triangular face

The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base is \( 5 \, \text{m} \) and the height (slant height) is \( 9 \, \text{m} \):
\( \text{Area of one triangle} = \frac{1}{2} \times 5 \times 9 = 22.5 \, \text{m}^2 \)

Step4: Calculate the total area of the four triangular faces

There are four identical triangular faces, so:
\( \text{Total Lateral Area} = 4 \times 22.5 = 90 \, \text{m}^2 \)

Step5: Calculate the total surface area

The total surface area is the sum of the base area and the total lateral area:
\( \text{Surface Area} = 25 + 90 = 115 \, \text{m}^2 \)

Answer:

\( 115 \)