Question

Find the area of a triangle, two sides of which are 8cm,11cm and the perimeter is 32cm

Answer 1

The area of triangle is b) $8 \sqrt{30} \ \mathrm{cm}^{2}$

Given:

Assume the triangle sides are a, b, and c.

a = 8 cm; b = 11 cm; and c = ?

Perimeter = 32 cm

To find:

Triangle area = ?

Step-by-step explanation:

The formula for area of triangle is $\sqrt{s(s-a)(s-b)(s-c)}$

Where s = semi perimeter

a, b, c are sides of triangle

Semi-perimeter, $\mathrm{s}=\frac{\text { Perimeter }}{2}$

$\mathrm{s}=\frac{32}{2}$

$s=16 \ \mathrm{cm}$

Since, the perimeter = 32 cm

So,

$a + b + c = 32$

$8+11+c=32$

$c=32-19$

$c=13$

$\text{Area of triangle} =\frac{\text { Perimeter }}{2}$

$=\sqrt{16(16-8)(16-11)(16-13)}$

$=\sqrt{8 \times 2 \times 8 \times 5 \times 3}$

$=8 \sqrt{2 \times 5 \times 3}$

$=8 \sqrt{10 \times 3}$

$\text{Area of triangle} =8 \sqrt{30} \ \mathrm{cm}^{2}$

Answer 2

Answer:

Step-by-step explanation:

Given:-

Side a = 8 cm

Side b = 11 cm

Side c = ???

Perimeter = 32 cm

To Find:-

Area of triangle

Solution:-

To find the area, we have to firstly find the all sides of triangle.

so, we know that

⇒ a + b + c = 32 cm

⇒ 8 + 11 + c = 32 cm

⇒ 19 + c = 32

⇒ c = 32 - 19

⇒ c = 13 cm

Area of triangle = √ (s (s-a) (s-b) (s-c) )

Here s is the semi-perimeter.

Semi-perimeter = Perimeter/2 = 32/2= 16 cm

Putting all the values, we get

⇒ √ (s (s-a) (s-b) (s-c) )

⇒ √(16 × (16−8) × ( 16−11) × (16−13))

⇒ √ (16 × 8 × 5 × 3)

⇒ √8 × 2 × 8 × 5 × 3

⇒ √8 × 8 × 2 × 5 × 3

⇒ 8 √ 2 × 5 × 3

= 8√30 cm²

Hence, Area of triangle is 8√30 cm².