Question

A block of wood has the shape of a triangular prism. The bases are right triangles. Find its surface area.

Answer 1

$\huge\mathbb{↑↑SOLUTION↑↑}$

Answer 2

We must recall that:

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms or rectangles without the bases. And the bases of the prism could be triangle, square, rectangle or any n-sided polygon.

In ΔABC

$AB^2+BC^2=AC^2$

$(1.5)^2+BC^2=(2.5)^2$

$BC^2=6.25-2.25$

$BC^2=4$

$BC=\sqrt{4}$

$BC=2$

Surace area of prism $=$ (perimeter of base × length of prism) + (2 × Area of bases)

$=6\times 12+2\times 1.5 \times 2 \times \frac{1}{2}$

$=72+3=75in^2$