Question

find the area of triangle using herons formula with measurement 9,9,14

Answer 1

Answer : A= hbh

2

b : base

hb : height

Answer 2

ANSWER:

Given:

• Length of sides of triangle = 9units, 9units and 14units.

To Find:

• Area of the triangle.

Diagram:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\put(1.7,1.5){ \bf 9 }\put(4.1,1.5){ \bf 9 }\put(3,-0.3){ \bf 14 }\end{picture}$

Solution:

Let the sides of the triangle be a, b and c.

We know that, by Heron's Formula,

$\hookrightarrow\sf Area=\sqrt{s(s-a)(s-b)(s-c)\,}$

Here,

⇒ a = 9 units, b = 9 units, c = 14 units and s = semi-perimeter

$\implies\sf s=\dfrac{Perimeter}{2}=\dfrac{a+b+c}{2}$

$\implies\sf s=\dfrac{9+9+14}{2}$

$\implies\sf s=\dfrac{32\!\!\!\!\!/^{\:\:16}}{2\!\!\!/}$

$\implies\sf s=16$

So, the area of the triangle is,

$\implies\sf Area=\sqrt{s(s-a)(s-b)(s-c)\,}$

$\implies\sf Area=\sqrt{16(16-9)(16-9)(16-14)\,}$

$\implies\sf Area=\sqrt{16\times7\times7\times2\,}$

$\implies\bf Area=28\sqrt{2}$

Therefore the Area of the triangle is 28√2 square units.

Formula Used:

$\hookrightarrow\sf Area=\sqrt{s(s-a)(s-b)(s-c)\,}$