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The base of an even solid prism is a triangle whose sides are 6, 8 and 10 cm. The height of the prism is 10 cm. What will be the total surface area, lateral surface area and volume of the prism?

The base of an even solid prism is a triangle whose sides are 6, 8 and 10 cm. The height of the prism is 10 cm. What will be the total surface area, lateral surface area and volume of the prism? Correct Answer 288 sq cm, 240 sq cm, 240cubic cm

Solution:

Given: Lateral height (L) = 10 cm

Hypotenuse (a) = 10 cm

Base of triangle (b) = 8 cm

Height of triangle (h or c) = 6 cm

Formula used: Total surface area = 2 + (a + b + c) × L

Lateral surface area = (a × L) + (b × L) + (c × L)

Volume = (1 / 2) (b) (h) × L

Calculation: Total surface area = 2 + (8 + 10 + 6) × 10

⇒ 2 + 24 × 10

⇒ 2 × 24 + 24 × 10

⇒ 48 + 240

⇒ 288

Lateral area = (10 × 10) + (8 × 10) + (6 × 10)

⇒ 100 + 80 + 60

⇒ 240

Volume = (1 / 2) (8) (6) × 10

⇒ 4 × 6 × 10

⇒ 240

∴ Total surface area = 288 cm2

Lateral surface area = 240 cm2

Volume = 240 cm3

 

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