Question

if the side of a triangle are 34cm,16cm, 28cm, find the area of the triangle​

Answer 1

$\huge\mathbb{ANSWER:-}$

$\sf\underline{\blue{\:\:\:\:\: Given:-\:\:\:\:\:}}$

Sides of ∆

=> 34cm ,16cm ,28cm

$\sf\underline{\pink{\:\:\:\:\: To\:Find:-\:\:\:\:\:}}$

The Area of triangle

• By heron's Formula

$\boxed{\sf{\sqrt{s(s-a)(s-b)(s-c)}}}$

$\sf\underline{\purple{\:\:\:\:\: Solution:-\:\:\:\:\:}}$

$\sf\implies s=\frac{a+b+c}{2}\\ \\ \sf\implies s=\dfrac{34+16+28}{2}\\ \\ \sf\implies \cancel{\dfrac{78}{2}}= 39\\ \\ \tt\implies semi\: perimeter=39cm$

• Now the area

$\sf\implies Area=\sqrt{39(39-34)(39-16)(39-28)}\\ \\ \sf\implies Area \sqrt{39\times 5\times 23\times 11}\\ \\ \sf\implies Area=\sqrt{49335}\\ \\ \sf\implies Area\:of\:\triangle =222.11cm{}^{2}$

$\underline{\fbox{\purple{\sf{Area\:of\: triangle=222.11cm{}^{2}}}}}$

Answer 2

Answer:

$\huge\underline\mathfrak\pink{holamate}$

$\sf\underline{\green{\:\:\:\:\:Given:-\:\:\:\:\:}}$

First side of a triangle=34cm

Second side of a triangle=16cm

Third side of a triangle=28cm

$\sf\underline{\red{\:\:\:\:\:To find:-\:\:\:\:\:}}$Area of the triangle

$\sf\underline{\orange{\:\:\:\:\:Formula used:-\:\:\:\:\:}}$

• Heron's formula

Area of triangle=√s(s-a)(s-b)(s-c)

• Perimeter of a triangle=Sum of all sides
• Semi-Perimeter=Perimeter/2

$\sf\underline{\blue{\:\:\:\:\: Solution:-\:\:\:\:\:}}$

Perimeter of a ∆ = sum all sides

P=(34+16+28)cm

P=78cm

Semi-Perimeter=Perimeter/2

S=78/2

S=39cm

By using Heron's formula ,

Area of a ∆=√s(s-a)(s-b)(s-c)

=√[ 39 (39-34) (39-16) (39-28) ]

=√[ 39 × 5 × 23 × 11 ]

=√[ 3 × 13 × 5 × 23 × 11]

=√49,335 cm sq.

=221.114 cm sq.

$\sf\underline{\purple{\:\:\:\:\:Area of a triangle :-\:\:\:\:\:}}$2221.114 cm sq.

$\huge\underline\mathfrak\green{thanks}$