Question

The base of a prism is a right angled triangle with two sides 5 cm and 12 cm. The height of the prism is 10 cm. The total surface area of the prism is ?​

Answer 1

Answer:

The base of a prism is a right angled triangle with two sides as 5 cm and 12 cm. The height of the prism is 10 cm. = 360 sq cm

Explanation:

In a right angle triangle prism ….we will have 2 right angle triangles and 3 rectangular faces

2 triangles faces = 1/2 × b × h

1/2 × 5 × 12 = 30 sq cm

2 triangles are having same dimensions

2 × 30 sq cm = 60 sq cm….(equation 1)

1st rectangle has length and breadth of 12 and 10 cm

Surface area = l × b

SA1 = 12 ×10 = 120 sq cm….(equation 2)

2nd rectangle has length and breadth of 13 and 10 cm

Surface area = l × b

SA 2 = 13 × 10 = 130 sq cm…..(equation 3)

3rd rectangle has length and breadth of 10 and 5 cm

Surface area = l × b

SA 3 = 10 × 5 = 50 sq cm….. (equation 4)

Now adding eq 1, eq 2, eq 3 ,eq 4

Total surface area = (60 + 120 + 130 + 50)sq cm

Total surface area = 360 sq cm

Answer 2

Answer:

Total surface area of the prism is 360 cm$^{2}$

Explanation:

Given:

• Base of the prism is a right angled trianlge with two sides 5 cm and 12 cm.

• Height of the prism is 10 cm.

To find:

Total surface area of the prism.

Solution:

Its total surface area will be the addition of lateral surface area + 2 × base area i.e. total surface area of the right angle prism = lateral surface area + 2 × base area.

Now as we know that ita lateral surface area will l( ${S_1}$ + ${S_2}$ + ${S_3}$ )

and base area will be 1/2 × b × h

So total surface area of the prism = l × ( ${S_1}$ + ${S_2}$ + ${S_3}$ ) + 2 (1/2 × b × h)

Now by substituting the values, we get

T.S.A of right angle prism

= 10 × (5 + 12 + 3) + 2 × 1/2 × 5 × 12

= 300 + 60

= 360 cm$^{2}$