Question

find the area of triangle when three sides of it is 10 cm 12cm18cm​

Answer 1

Step-by-step explanation:

Given:

Sides of triangle as 10 cm, 12 cm and 18 cm

To find: Find the area of triangle.

Solution:

Formula used:

Heron's formula

$\boxed{\bold{Area = \sqrt{S(S - a)(S - b)(S - c)}}}$

where, S is Semi-Perimeter of triangle and a,b and c are sides.

Step 1: Find S

$S = \frac{10 + 12 + 18}{2} \\ \\ S = \frac{40}{2} \\ \\\bold{ S= 20}$

Step 2: Find area of triangle

$Area = \sqrt{20(20 - 10)(20 - 12)(20 - 18)} \\ \\ Area = \sqrt{20 \times 10 \times 8 \times 2} \\ \\ Area= \sqrt{4 \times 5 \times 5 \times 2 \times 4 \times 2 \times 2} \\ \\Area = \sqrt{ {4}^{2} \times {5}^{2} \times {2}^{2} \times 2 } \\ \\ Area= 4 \times 5 \times 2\sqrt{2} \\ \\Area= 40 \sqrt{2} \: {cm}^{2}$

Final answer:

Area of triangle is 40√2 cm² or 56.56 cm².

Hope it helps you.

Answer 2

Given :   three sides of triangle  10 cm 12cm 18cm​

To Find   :  area of triangle

Solution:

sides of triangle  10 cm 12cm 18cm​

a = 10

b = 12

c = 18

s = semi perimeter = (10 + 12 + 18)/2  =  20

Area of Triangle  = √s(s-a)(s-b)(s-c)

= √20(20-10)(20-12)(20-18)

= √20 * 10 * 8 * 2

= √20 * 20 * 2 * 2 * 2

= 40√2

Area of Triangle = 40√2 cm²

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