Question

An isosceles A has perimeter 30cm and each
of the equal sides is 12 cm. Find the area of triangle​

Answer 1

Given :

• Perimeter is 30 cm
• Two side is 12 cm

To find :

• Area of triangle

According to the question,

Let the third side be x

→ 12 + 12 + x = 30

→ 24 + x = 30

→ x = 30 - 24

.°. x = 6 cm

Now we will use Heron's Formula,

$\sf{s = \frac{a + b + c}{2} }$

$\sf{s = \frac{12 + 12 + 6}{2} }$

$\implies\sf{ \cancel\frac{30}{2} = 15 \: cm} \green \bigstar$

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

$\implies\sf{ \sqrt{15(15 - 12)(15 - 12)(1 - 6)} }$

$\implies\sf{ \sqrt{15 (3)(3)(9)} }$

$\implies\sf{ \sqrt{3 \times 5 \times 3 \times 3 \times 3 \times 3} }$

$\implies\sf{ 3 \times 3\sqrt{15} }$

$\therefore\sf{ 9\sqrt{15} \: {cm}^{3} } \green\bigstar$

More details :-

The formula given by Heron about the area of a triangle,is also known as Hero's formula. It is stated as :

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

where a,b and c are the sides of the triangle, and s = semi - perimeter. [ half the perimeter of the triangle $\sf{s = \frac{a + b + c}{2} }$

Answer 2

Given :-

• An isosceles A has perimeter 30cm and each of the equal sides is 12 cm.

To find:-

• Find the area of triangle.

SOLUTION:-

Let the third side be x

➝ 12 + 12 + x = 30

➝ 24 + x = 30

➝ x = 30 - 24

➜ x = 6 cm.

We know ,

Heron's formula :

$\sf \pink{\boxed{✯Area = \sqrt{s(s - a)(s - b)(s - c)}}}$

Where,

$\sf ☆ \orange{s = \frac{a + b + c}{2} }$

And , a,b,c are sides of triangle

& s= semi-perimeter

$\implies \sf{s = \frac{12 + 12 + 6}{2} }$

$\implies\sf{ \cancel\frac{30}{2} = 15 \: cm}$

$\implies\sf{ \sqrt{s(s - a)(s - b)(s - c)} }\\ \\ \\ </p><p> \implies\sf{ \sqrt{15(15 - 12)(15 - 12)(1 - 6)} }\\ \\ </p><p>\implies\sf{ \sqrt{15 (3)(3)(9)} }\\ \\ \\ </p><p> \implies\sf{ \sqrt{3 \times 5 \times 3 \times 3 \times 3 \times 3} }\\ \\ \\ </p><p> \implies\sf{ 3 \times 3\sqrt{15} }$

$\therefore \sf \boxed{\pink{ 9\sqrt{15} \: {cm}^{3} }}$

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