Volume of triangular prism = Base area x height
Problem 1 :
Find the volume of the triangular prism given below.
Solution :
Base area = (1/2) x base x height
= (1/2) x 12 x 8
= 48
Volume = baes area x height of the prism
= 48 x 20
V = 960 cm³
Problem 2 :
Find the
(i) Total surface area
(ii) Volume
of the triangular prism given below.
Solution :
(ii) Total surface area :
Area of triangle = 2(1/2) × b × h
= 12 × 10
Area of triangle = 120 cm² --- > (1)
Area of rectangle = b × h
= 20 × 12
= 240 cm²
Area of three rectangle = 3 × b × h
= 3 × 240
= 720 cm² --- > (2)
Add (1) & (2)
Total surface area = 120 + 720
= 840 cm²
So, surface area of triangular prism = 840 cm²
(ii) Volume = Base area x height
= 120 x 20
= 2400 cm^{3}
Problem 3 :
The height of a triangular prism is 6 cm and its base is an equilateral triangle of side 5 cm. Find the volume of the prism.
Solution :
Volume of triangular prism (V) = Base area x height
Base is in the shape of equilateral triangle,
Area of equilateral triangle = √3/4 × a²
Base area = √3/4 × 5² = √3/4 × 25 Base area = 6.25 √3 cm² |
Volume = A × h = 6.25 √3 × 6 = 37.5 √3 (√3 = 1.732) = 37.5 × 1.732 = 64.95 cm³ |
So, volume of triangular prism = 64.95 cm³
Problem 4 :
A right prism stands on a base which is a right triangle with legs 3 cm and 4 cm. find the volume of the prism if its height is 9 cm.
Solution :
Given, side a = 3 cm and b = 4 cm
Using Pythagoras theorem,
a² + b² = c² 3² + 4² = c² c = √(9 + 16) c = √25 c = 5 cm |
Perimeter of a triangle = (3 + 4 + 5) / 2 = 12/2 = 6 cm |
Area of
triangle = √s(s - a)(s - b)(s - c)
= √6 (6 - 3)(6 - 4)(6 - 5)
= √6(3)(2)(1)
= √36
= 6 cm²
Volume of right prism = Base area × height
= 6 × 9
= 54 cm³
So, volume of triangular prism = 54 cm³
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM