Question

you correctly chose a square pyramid.
find the surface area of the
square pyramid.
first, find the area of
1 triangle.
(area = bh÷2)
1 triangle: ? ft2
4 triangles ft2
ft2
ft2
12 ft
10 ft
10 ft

Explanation:

Step1: Calculate the area of one triangle

The formula for the area of a triangle is \(A = \frac{bh}{2}\). Here, the base \(b = 10\) ft and the height \(h=12\) ft.

$$A_1=\frac{10\times12}{2}=60$$

Step2: Calculate the area of four triangles

Since there are 4 congruent triangular faces, \(A_{triangles}=4\times A_1\)

$$A_{triangles}=4\times60 = 240$$

Step3: Calculate the area of the square base

The area of a square is \(A = s^2\), where \(s = 10\) ft.

$$A_{base}=10\times10=100$$

Step4: Calculate the total surface area

The total surface area \(A_{total}=A_{triangles}+A_{base}\)

$$A_{total}=240 + 100=340$$

Answer:

1 Triangle: \(60\) \(ft^2\)
4 Triangles: \(240\) \(ft^2\)
Base: \(100\) \(ft^2\)
Total Surface Area: \(340\) \(ft^2\)