Question

Q1.Each side of an equilateral triangle is 8 cm. find a) Area of triangle b) Height of the triangle.

class9 ch12 Heron's formula ncert​.

Answer 1

Explanation:

Given:

An equilateral triangle with -

Each side = 8 cm

What To Find:

We have to -

a. Find the area of the triangle.

b. Find the height of the triangle.

Formulas Needed:

The formulas are -

$\begin{gathered}\bf \to Area = \sqrt{s(s-a)(s-b)(s-c)} \: \: ... (Heron's \: Formula)\\ \\ \bf {\to Area = \dfrac{1}{2} \times b \times h \: \: ... (Simple \: Formula)}\end{gathered} </p><p></p><p> </p><p>$

Abbreviations Used:

For Heron's Formula -

s = semi-perimeter

a = 1st side

b = 2nd side

c = 3rd side

For Simple Formula -

b = base

h = height

Solution:

Finding the area using Heron's formula.

First, find the s.

$\sf \to S = \dfrac{Sum \: of \: all \: sides}{2}$

$\sf \to S = \dfrac{8+8+8}{2}</p><p> </p><p>$

$\sf \to S = \dfrac{24}{2}$

S=12cm

Next, find the area.

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

$\sf \to Area = \sqrt{12(12-8)(12-8)(12-8)}</p><p>$

$\sf \to Area = \sqrt{12(4)(4)(4)}$

$\sf \to Area = \sqrt{768}$

$\sf \to Area = 27.7 \: cm^2 \: approx</p><p>$

Finding the height.

$\sf \to Area = \dfrac{1}{2} \times b \times h$

$\sf \to 27.7 = \dfrac{1}{2} \times 8 \times h</p><p>$

$\sf \to \dfrac{27.7}{4} = </p><p>$

$\sf \to 6.925 \: cm =$

Final Answer:

• a. ∴ Thus, the area of a triangle is 27.7 cm² approx.
• b. ∴ Thus, the height of a triangle is 6.925 cm.