Question

the height of a triangular prism is 10 cm. the sides of the Base are 3cm,4 cm,5cm. then the T.S.A is​

Answer 1

Answer:

Hi Your Answer

Step-by-step explanation:

Given, sides of prism are 3 cm, 4 cm and 5 cm and height =10 cm

Let s be the semi-perimeter of the triangular base of the prism.

Then S=

2

3+4+5

=6 cm

Therefore, the area of the prism =

s(s−a)(s−b)(s−c)

=

6(6−3)(6−4)(6−5)

=

6×3×2×1

=

36

=6 sq. cm.

Then volume of the prism =area of base×height

= 6×10

= 60 cu.cm

Answer 2

Given:

height of the triangular prism = 10cm

measure of sides of the base = 3cm,4cm and 5cm

To Find:

total surface area of the triangular prism

Solution:

As we know that:

➙ total surface area (T.S.A) = B + P × h

★ B = area of the base

★ p = perimeter of the base

★ h = height of the prism

Here:

base is a right angled triangle (because 3,4,5 is a triplet)

base and height will be 3,4 cm or 4,3cm and 5 is hypotenuse.

So, formulae for B:

$⟹B = \frac{1}{2} \times base \times height$

$⟹B = \frac{1}{2} \times 3 \times 4 = {6cm}^{2}$

So,

total surface area = 6 + (3 + 4 + 5) × 10

total surface area = 6 + 120 = $\tt\underline\red{126\:cm²}$

Hence:

• total surface area of the triangular prism is 126cm²