Question

A decorative stone for home decor is in the shape of triangular pyramid, whose base is an equilateral triangle. Find the surface area of the stone.

• A. 22.5 sq in
• B. 26.4 sq in
• C. 60 sq in
• D. 45 sq in

Answer 1

The correct option is B 26.4 sq in

The stone is in the shape of a triangular pyramid.

It has one triangular base and 3 triangular lateral faces.

Total surface area of the given pyramid = Base area + surface area of 3 triangular faces.

Area of triangle = $\frac{1}{2}$ $\times$ base $\times$ height

Base of the base triangle = 3 in

Height of the base triangle = 2.6 in

Area of the base triangle = $\frac{1}{2}$ $\times$ 3 $\times$ 2.6 = 3.9 sq in

Area of a triangular face = $\frac{1}{2}$$\times$ base $\times$ height

Base of the triangle =3 in

Height of the triangle = 5 in

Area = $\frac{1}{2}$ $\times$3 $\times$ 5 = 7.5 sq in

Total area of 3 triangular faces = 3 $\times$ 7.5 = 22.5 sq in

Base area = 6 sq in

Total surface area of the triangular pyramid = Base area + Area of the 3 triangular faces

= 3.9 + 22.5 = 26.4 sq in

Hence, the surface area of the stone = 26.4 sq in