Question

Jennifer got a box of chocolates. The box is a right triangular prism shaped box. it is 7 inches long, and the triangular base measures 2in*3in*4in. What is the surface area of the box of chocolates?

Answer 1

Solution:

Area of two triangular bases can be calculated by using heron's formula.

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}, where ,s=\frac{a+b+c}{2}$

$s=\frac{2+3+4}{2}=\frac{9}{2}=4.5\\\\ Area(\Delta)=\sqrt{4.5(4.5-2)(4.5-3)(4.5-4)}=\sqrt{4.5 \times 2.5 \times1.5 \times 0.5}=\sqrt{2.25 \times 3.75}=1.5 \times 0.5 \sqrt{15}\\\\ Area(\Delta)=0.75 \times 3.8729=2.90$

Area of three quadrilateral shapes which is in the shape of rectangle =

2 × 7 + 3 × 7 + 4 ×7

= 14 +21+28

=63 square inches

Area of two triangular base= 2.90 × 2= 5.80 square inches

Total surface area of box which is in the form of right triangular prism = 63 +5.80= 68.80 square inches