Question

The base of an iso seceles triangle is 8cm
each of the equal side is 5 cm - Find the
arop of the triangle in heronce formula with explain ​

Answer 1

$\Large {\underline { \sf \orange{Appropriate \: Question :}}}$

The base of an isosceles triangle is 8cm each of the equal side is 5 cm. Find the area of the triangle in heron's formula.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

Given:

• Base of the isosceles triangle = 8 cm

• Equal sides = 5 cm

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To calculate :

• Area of the triangle using Heron's formula.

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Calculation :

We know that as per the Heron's formula,

★ Area of ∆ = √s(s-a)(s-b)(s-c)

• s = Semi-perimeter ⇒ $\sf { \dfrac{a+b+c}{2}}$

Calculating Semi-perimeter

→ Semi-perimeter = $\sf { \dfrac{a+b+c}{2}}$

→ Semi-perimeter = $\sf { \dfrac{5+5+8}{2} \: cm}$

→ Semi-perimeter = $\sf { \dfrac{18}{2} \: cm}$

→ Semi-perimeter = $\sf { \dfrac{18}{2} \: cm}$

→ → Semi-perimeter = 9 cm

Now, calculating area :

★ Area of ∆ = √s(s-a)(s-b)(s-c)

→ Area of ∆ = √9(9-5)(9-5)(9-8) cm²

→ Area of ∆ = √(9 × 4 × 4 × 1) cm²

→ Area of ∆ = √(3 × 3 × 4 × 4) cm²

• Making pairs and picking up a factor form each pair.

→ Area of ∆ = (3 × 4) cm²

→ Area of ∆ = 12 cm²

Therefore, area of the isosceles triangle is 12 cm².

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$\Large {\underline { \sf \orange{Know \: More!}}}$

Important properties of triangle :

★ Angle sum property of a triangle :

• Sum of interior angles of a triangle = 180°

★ Exterior angle property of a triangle :

• Sum of two interior opposite angles = Exterior angle

★ Perimeter of triangle :

• Sum of all sides

★ Area of triangle :

• $\sf { \dfrac{1}{2} \times Base \times Height }$

★ Area of an equilateral triangle:

• $\sf { \dfrac{\sqrt{3}}{4} \times {Side}^{2} }$

★ Area of a triangle when its sides are given :

• $\sf { \sqrt{s(s-a)(s-b)(s-c)} }$

Where,

• S= Semi-perimeter
• Or $\sf {\dfrac{a+b+c}{2} }$