Question

Find the area of a triangle whose sides are 12 cm, 6 cm and 15 cm.

2.   Find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 cm.

plz answer it

Answer 1

1.

The given sides are 12cm, 6cm and 15cm.

Let a = 12 cm
b = 6 cm
c = 15 cm

Semi-perimeter =( a + b + c) / 2

S = 12 + 6 + 15 / 2

s = 43 / 2

s = 21.5

So, using the Heron's Formula, i.e.,

$\bf \: = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{21.5(21.5 - 12)(21.5 - 6)(21.5 - 15)} \\ \\ = \sqrt{21.5(9.5)(15.5)(6.5)} \\ \\ = \sqrt{2010330.62} \\ \\ = 1417.87 {cm}^{2}$

2.

Given the two sides of triangle are 4.5 cm and 10 cm
Perimeter = 10.5 cm

semi-perimeter = perimeter / 2

s = 10.5 / 2

s = 4.25

Letting a = 4.5 cm
b = 10 cm
c = (to be calculated)

We know that,

$\bf \: a + b + c = perimeter$

4.5 + 10 + c = 10.5

14.5 + c = 10.5

c = 10.5 - 14.5

c = - 4

Using Heron's Formula,

$= \sqrt{s(s - a)(s - b)(s - c) } \\ \\ = \sqrt{4.25(4.25 - 4.5)(4.25 - 10)(4.25 + 4)} \\ \\ = \sqrt{4.25( - 0.25)( - 5.75)(8.25) } \\ \\ = \sqrt{50.41} \\ \\ = 7.1 {cm}^{2}$

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