Question

in the triangle ABC 12 cm and height is 5 cm find the area of the triangle with the help of heron's formula​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:triangle=30\:cm^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Base = 12 \: cm \\ \\ \tt: \implies Height= 5 \: {cm} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Area\:of\:triangle = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \tt: \implies {h}^{2} = {5}^{2} + {12}^{2} \\ \\ \tt: \implies {h}^{2} =25 + 144 \\ \\ \tt: \implies {h}^{2} = {169} \\ \\ \tt: \implies {h}= \sqrt{169} \\ \\ \green{\tt: \implies {h} =13 \: cm} \\ \\ \bold{According \: to \: heron's \: formula} \\ \tt: \implies s = \frac{a + b + c}{2} \\ \\ \tt: \implies s = \frac{5 + 12 + 13}{2} \\ \\ \tt: \implies s = \frac{30}{2} \\ \\ \green{\tt: \implies s =15} \\ \\ \bold{For \: Area \: of \: triangle} \\ \tt: \implies Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{15 \times 10 \times 3 \times 2 } \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{900} \\ \\ \green{\tt: \implies Area \: of \: triangle = 30 \: {cm}^{2} }$

Answer 2

$\tt{\huge{\orange {Hello!!! }}} B.Q.$

QUESTION :

in the triangle ABC 12 cm and height is 5 cm find the area of the triangle with the help of heron's formula

SOLUTION :

Given :

Base = 12 cm.

Height = 5 cm.

Hypotenuse = √ [ Base^2 + Height^2 ]

=> √ [ 12^2 + 5^2 ]

=> √ { 169 }

=> 13 cm .

Semiperimeter = [ a + b + c ] / [ 2 ] = [ 12 + 5 + 13 ] / [ 2 ] = 15

Area of Triangle = √ [ { s } { s - a } { s - b } { s - c } ]

=> √ [ { 15 } { 15 - 12 } { 15 - 5 } { 15 - 13} ]

=> √ [ 15 × 3 × 10 × 2 ]

=> 3 × 2 × 5

=> 30 cm^2

Hence the area of Triangle ABC = 30 cm^2.......(A)