Right triangular Prisms are one type of three dimensional solid shapes. Generally the flat surface of the triangular Prisms is called as its faces. The top and bottom faces are known as bases. Faces forming the sides are the lateral faces or lateral surfaces. Right triangular prisms have six vertices. Vertices are the corner points of triangular prism. let us see about how to calculate the surface area of the shapes.
Surface area of a right triangular prism:
Total surface area T.S.A = (P x h + 2 A) sq. units
P = perimeter of base (a + b + c)
h = height of the prism
A = Area of the base
Right triangular prisms- Example problem
1. The base of a prism is a right angled triangle of side 6 cm, 8cm and 10 cm. its height is 20cm.find total surface area of prism.
Solution:
Given:
The sides if the triangular are 6 cm, 8 cm and 10 cm
Height of the prism is 20 cm
Let us take the base of the right triangular prism = 6 cm
Height of the right triangular prism =20cm
Formula:
Total surface area T.S.A = (P x h + 2 A) sq. units
Perimeter (p) = a + b + c
= 8 + 6 + 10
= 24 cm
Area of the base (A) = ½ (base x height)
= ½ (6 x 20)
= 120/2
= 60 cm2
Substitute in the formula,
T.S.A = (24 x 20 + 2 x 60)
= 480 + 120
= 600 cm3
Total surface area T.S.A = 600 cm2
2. The base of a prism is a right angled triangle of side 9 cm, 12cm and 15 cm. its height is 15 cm. find total surface area of prism.
Solution:
Given:
The sides if the triangular are 9 cm, 12 cm and 15 cm
Height of the prism is 15 cm
Let us take the base of the right triangular prism = 9 cm
Height of the right triangular prism =15cm
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Formula:
Total surface area T.S.A = (P x h + 2 A) sq. units
Perimeter (p) = a + b + c
= 9 + 12 + 15
= 36 cm
Area of the base (A) = ½ (base x height)
= ½ (9 x 15)
= 135/2
= 67.5 cm2
Substitute in the formula,
T.S.A = (36 x 15 + 2 x 67.5)
= 540 + 135
= 675 cm3
Total surface area T.S.A = 675 cm2
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