Question

69.
in the pyramid above, each triangular face has
the same area, and the base mnpq is a
square that measures 8 centimeters on each
side. if the length of \\( \overline { r s } = 6 \\) centimeters, what
is the surface area of the pyramid excluding
the base?
a. 48 sq cm
b. 96 sq cm
c. 128 sq cm
d. 160 sq cm

Explanation:

Step1: Calculate the area of one triangular face

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of each triangular face is \(8\) cm (side of the square base) and the height (slant height) is \(RS = 6\) cm.
So, \(A=\frac{1}{2}\times8\times6=24\) \(cm^{2}\)

Step2: Calculate the total area of the four triangular faces

Since there are \(4\) triangular faces (because the base is a square) and each has an area of \(24\) \(cm^{2}\)
The total surface area (excluding the base) is \(4\times24 = 96\) \(cm^{2}\)

Answer:

B. \(96\) \(sq\) \(cm\)