Question

The base of a prism is a rectangle of sides 24 cm and 7 cm respectively and its height is 30 cm. It is split vertically along the diagonal of the base into two triangular prisms. What is the total surface area of each of the triangular prisms?

• A. $1848c{m}^2$
• B. $1948c{m}^2$
• C. $1928c{m}^2$
• D. $1826c{m}^2$

Answer 1

The correct option is A

$1848c{m}^2$

Base of the prism has length and breadth 24 cm and 10 cm respectively.

Diagonal of base $=\sqrt{{24}^2+7^2}$

$=\sqrt{576+49}$

$=\sqrt{625}=25cm$

Total surface area will be equal to

Total surface area = Lateral surface area + area of the top and bottom triangles

Total surface area = Area of rectangle + $2\times \text{Area of triangle}$

$=24\times 30+7\times 30+25\times 30+2\times \frac{1}{2}\times 24\times 7$

$=30(24+7+25)+24\times 7$

$=30\times 56+168$

$=1680+168$

$=1848c{m}^2$