Question

find semi perimeter and then area of triangle
side - 10 , 8 and 12​

Answer 1

Given :-

• Sides :-

• a = 10cm
• b = 8cm
• c = 12 cm

Solution :-

Diagram

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

As we all know ,

The perimeter of Triangle ↬ sum of all sides

Perimeter ↬ ( a + b + c )

From given

➤ a = 24 cm

➤ b = 7 cm

➤ c = 25 cm

Now,

Applying the Heron's Formula

$\bold{According \: to \: heron's \: formula} \\ \tt: \implies s = \frac{a + b + c}{2} \\ \\ \tt: \implies s = \frac{10 + 8 + 12}{2} \\ \\ \tt: \implies s = \frac{30}{2} \\ \\ \bf{\tt: \implies s = 15}$

Here s is the half perimeter ( semi perimeter )

Lets find area of triangle now ,

$\bold{For \: Area \: of \: triangle} \\ \tt: \implies Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{15(15 - 10)(15 - 8)(15 - 12)} \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{15 \times 5 \times 7\times 3 } \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{1575} \\ \\ \bf{\tt: \implies Area \: of \: triangle = 39.68 \: {cm}^{2} }$

_______________________

Answer 2

Answer:

semi perimeter = (side 1 + side 2 + side 3 ) /2

= ( a+b+c) /2

=( 10+8+12) /2 units

= 30/2 units

= 15units

area = √ {s ( s-a) (s-b) (s-c) } sq. units

= √ { 15( 15-10) (15-8) (15-12) } sq. units

= √ { 15( 5× 7×3) }sq.units

= √ { 15(105) }sq.units

=√ 1575 sq. units

= 39.68 sq. units