Answer:
The volume of the prism is 243 cm³
Step-by-step explanation:
The volume of the prism is V = B × H, where
- B is the area of its base
- H is the height of the prism
∵ The prism is a triangular prism
∴ Its base is a triangle
∵ The base of it is a right triangle
∴ Its area B = [tex]\frac{1}{2}[/tex] b h, where b and h are the legs of the right angle
→ We have one leg of the right angle and the hypotenuse, so we
must use the Pythagoras Theorem to find the other leg
∵ (5.4)² + h² = (7.8)²
∴ 29.16 + h² = 60.84
→ subtract 29.16 from oth sides
∴ h² = 31.68
→ Take √ for both sides
∴ h = 5.6284989 cm
→ Now find the area of the base
∵ B = [tex]\frac{1}{2}[/tex] (5.4)(5.6284989)
∴ B = 15.196947 cm²
→ Let us use the rule of the volume above
∵ V = B × H
∵ H = 16 cm
∴ V = 15.196947 × 16
∴ V = 243.151153 cm³
→ Round it to 3 significant figures
∴ V = 243 cm³
∴ The volume of the prism is 243 cm³
