Question

Find the area of isosceles triangle whose equal side are 6cm,6cm,and 8cm

Answer 1

Answer:

The area of the isosceles triangle is ⁸√5cm.

Step-by-step explanation:

Given side of the triangle :

• 6cm, 6cm & 8cm

Find the area :

Step 1 : Calculate the semi-perimeter

Semi-perimeter : (sum of three sides ÷ 2)

→ (6 + 6 + 8) ÷ 2

→ 20 ÷ 2

→ 10cm.

Step 2 : Calculate the area :

By Heron's formula :

→ √s(s - a)(s - b)(s -c)

Where,

• a, b, and c denotes the three respective sides of the triangle
• s is the semi-perimeter.

So,

→ √10(10 - 6)(10 - 6)(10 - 8)

→ √10(4)(4)(2)

→ √320

→ ⁸√5 cm.

The area of the triangel is ⁸√5cm.

Answer 2

Given : Equal sides of an isosceles triangle are 6cm, 6cm and 8cm respectively.

To Find : Area of the isosceles triangle.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀_____________________

Here

$\: \:$

• first side of the triangle, a = 6
• second side of the triangle, b = 6
• third side of the triangle, c = 8

$\:$

As we know that :

$\:$

$\star \: \underline{\boxed{\sf\purple{Area \: of \: a \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} }}}$

$\:$

★ Now, we'll find S (semi-perimeter) of the triangle.

$\:$

$\sf:\implies \: S_{(semi-perimeter)} = \dfrac{a + b + c}{2} \\ \\ \\ \sf:\implies \: S_{(semi-perimeter)} = \frac{6 + 6 + 8}{2} \\ \\ \\ \sf:\implies S_{(semi-perimeter)} = \cancel\frac{20}{2} \\ \\ \\ \sf:\implies \underline{\boxed{\mathfrak\purple{S_{(semi-perimeter)} = 10}}}\bigstar$

$\:$

Now we've to find the area of the triangle.

So, put the values in the area of the triangle formula and solve.

$\:$

$\sf:\implies \: Area_{(triangle)} = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \\ \sf:\implies Area_{(triangle)} = \sqrt{10(10 - 6)(10 - 6)(10 - 8)} \\ \\ \\ \sf:\implies Area_{(triangle)} = \sqrt{10 \times 4 \times 4 \times 2} \\ \\ \\ \sf:\implies Area_{(triangle)} = \sqrt{320} \\ \\ \\ \sf:\implies \underline{\boxed{\mathfrak\purple{Area_{(triangle)} = 8 \sqrt{5} {cm}^{2} }}} \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: area \: of \: the \: isosceles \: triangle \: is \: \bold{8 \sqrt{5} {cm}^{2}. }}}$