Question

find the area and perimeter​

Answer 1

Question :-

Find the area and the perimeter of the triangle whose three sides measures 6 cm, 6 cm and 10 cm.

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Solution :-

➲ Given Information :-

• 1st side of the triangle (a) ➢ 6 cm
• 2nd side of the triangle (b) ➢ 6 cm
• 3rd side of the triangle (c) ➢ 10 cm
• Given triangle is isosceles triangle

➲ To Find :-

• Perimeter of the triangle
• Area of the triangle

➲ Fomula Used :-

• Heron's Formula i.e., $\boxed{\bf area = \sqrt{s(s - a)(s - b)(s - c)}}$
• Perimeter = Sum of all sides of a triangle

➲ Concept :-

• Area And Perimeter of Figures

➲ Explanation :-

• Adding up all the sides of the triangle, We will get it's perimeter.
• We'll divide the perimeter by 2 in order to find its semi perimeter and then substitute the values of each side in the Heron's formula. Simplifying it, We will get our answer i.e., Area.

➲ Calculation :-

• Firstly Finding the Perimeter of the triangle.

∵ Perimeter of triangle = Sum of all the 3 sides

Substituting the values in the formula, We get,

⇒ Perimeter = a + b + c

⇒ Perimeter = 6 + 6 + 10

⇒ Perimeter = 22 cm

⇒ 22 cm is the perimeter

• Now, finding the area of the triangle.

Using Heron's Formula, We get,

⇒ $\boxed{\sf area = \sqrt{s(s - a)(s - b)(s - c)}}$

Finding (s) = semi perimeter

⇒ $\sf{\dfrac{perimeter}{2} = \dfrac{22}{2} = 11 cm}$

Substituting the values in the formula, We get,

⇒ $\sf area = \sqrt{11(11 - 6)(11 - 6)(11 - 10)}$

⇒ $\sf area = \sqrt{11(5)(5)(1)}$

⇒ $\sf area = \sqrt{11(25)}$

⇒ $\sf area = \sqrt{275}$

⇒ Area = $\bf \sqrt{275} \: cm²$ or 16.58 cm² or $\bf 5\sqrt{11}\: cm²$

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Final Answers :-

• Perimeter of the triangle = 22 cm
• Area of the triangle = $\bf \sqrt{275} \: cm²$ or 16.58 cm² or $\bf 5\sqrt{11}\: cm²$

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Answer 2

Answer:

hey mate!

here is the answer hope you find it helpful