Question

Angel is decorating the outside of a box in the shape of a triangular pyramid. The figure below shows a net for the box. If all the triangles are equilateral, what is the surface area of the box, in square centimeters, that Angel decorates?

Answer 1

Step 1

Find the base area of the triangle of sides 12cm, by 12cm by 12cm using heron formula.

`\begin{gathered} \text{a = 12, b = 12, c = 12} \\ \text{s = }(a+b+c)/(2)\text{ = }(12+12+12)/(2)=\text{ }(36)/(2)\text{ = 18} \\ Area\text{ of the base = }√(s(s-a)(s-b)(s-c)) \\ \text{= }√(18(18-12)(18-12)(18-12)) \\ =\text{ }√(18*6*6*6) \\ =\text{ 62.35} \end{gathered}`

Step 2

Find the area of the three triangular faces.

`\begin{gathered} Area\text{ of a triangle = }\frac{Base\text{ }*\text{ Height}}{2} \\ =\text{ }\frac{12\text{ }*10.39}{2} \\ =\text{ 62.34} \\ Area\text{ of the three faces = 3 }*\text{ 62.34 = 187.02 cm}^2 \end{gathered}`

A = 62.35 + 187.02 = 249.37

Final answer

A = 249.36

Method 2