Question

A solid rectangle has length, breadth and height = 15 cm, 8 cm & 20 cm respectively. It is cut into two triangular prisms along the diagonal as shown in the figure. The Total surface area of each prism will be equal to:

• A. $980c{m}^2$
• B. $960c{m}^2$
• C. $920c{m}^2$
• D. $1020c{m}^2$

Answer 1

The correct option is C

$920c{m}^2$

The rectangular figure is cut along its diagonal. Hence the third side of the triangle formed at the base can be calculated as:

$AC=\sqrt{(8{)}^2+(15{)}^2}$

$AC=\sqrt{64+225}$

$AC=\sqrt{289}$

$AC=17cm$

Total surface area of each triangular prism = Lateral Surface Area + $2\times Basearea$

Lateral Surface Area = $Height\times BasePerimeter$ $=20(8+15+17)c{m}^2$

Total Surface Area $=20(8+15+17)+8\times 15$

$=20\times 40+120$

$=800+120$

$=920c{m}^2$

Hence the Total Surface Area of each triangular prism $=920c{m}^2$