Question

the figure below is a net for a triangular pyramid.

if all the triangles are equilateral, what is the surface area of the pyramid, in square meters?

Explanation:

Step1: Calculate the area of one small equilateral triangle

The formula for the area of a triangle is \(A = \frac{1}{2}\times base\times height\). For a small equilateral triangle, base \(b = 6\div2= 3\)m (since the side of the large equilateral triangle is composed of two sides of small equilateral triangles), height \(h = 5.2\)m.

$$A_{small}=\frac{1}{2}\times3\times5.2=\frac{1}{2}\times15.6 = 7.8\space m^{2}$$

Step2: Count the number of small equilateral triangles

The net of the triangular pyramid (which is a tetrahedron in this case as all faces are equilateral triangles) is composed of \(4\) small equilateral triangles.

Step3: Calculate the surface area of the pyramid

$$A = 4\times A_{small}$$

Substitute \(A_{small}=7.8\) into the formula:

$$A = 4\times7.8=31.2\space m^{2}$$

Answer:

\(31.2\)