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Can a triangle and a Circle have the same perimeter?

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  • Last Updated : 30 Nov, 2021

Mensuration is a part of mathematics that deals with the study of geometric figures and calculation of its parameters like area, length, volume, perimeter, surface area, etc. The study deals with two-dimensional and three-dimensional shapes in which 2D shapes involve the length and breadth of the shape. It does not deal with the thickness of the shape. And, 3D shapes have dimensions of length, width, and height.

Formula chart for mensuration formulas 

The determination of parameters in the mensuration of different shapes takes place with the help of standard derived formulas. These formulas make the calculation more convenient for deriving the solution. 

2D shapes Formulas
Triangle 1/2 base × height
Rectangle

perimeter = 2(length + breadth)

Area = length × breadth

Square

Area = (side)2

Perimeter = 4(side)

Circle

Diameter = 2 × radius

Area = πr2

3D shapes Formulas
Sphere

Volume = 4/3πr3

Total surface area = πr(l + radius)

Cube

Volume = (side)3

Lateral surface area = 4(side)2

 Total surface area = 6(side)2

Cuboid

Volume = length × width × height

Lateral surface area = 2h(l + b)

Total surface area = 2(lb + lh + bh)

Cone 

Volume = 1/3 πr2h

Total surface area = πr(l + radius)

Can a triangle and a circle have the same perimeter?

Answer:

An equilateral triangle and a circle do not have the same perimeter. Let Pt  be the perimeter of an equilateral triangle, and, Pc is the perimeter of a circle. Now, evaluate the perimeter of an equilateral triangle and a circle.

The perimeter of an equilateral triangle by standard mensuration formula,

Pt  = a + b + c 

As the given triangle is equilateral it’s all sides are equal.

Pt = x + x + x

Pt = 3x

x = Pt/3

Circumference or perimeter of the circle,

Pc = 2πr

x = Pc/2π

The perimeter of the triangle is greater than a circle.

The perimeter of the triangle > Perimeter of the circle

Pt > Pc

Hence, the perimeter of an equilateral triangle and a square are the same.

Sample Problems

Question 1: If a circle has a radius of 14cm. Find its area.

Solution:

Given,

Radius of circle(r) =14cm

Area(A) = ?

Now,

Area = πr2

A = 22/7 × 14 × 14

A = 22 × 2 × 14

A = 616cm2

Hence, the area of given circle is 616 cm2.

Question 2: A rhombus has diagonals with lengths 5cm and 8cm respectively. Calculate its area.

Solution:

Given,

Diagonal 1(d1) = 5cm

Diagonal 2(d2) = 8cm

Now,

Area of rhombus(A) = 1/2 × d1 × d2

A = 1/2 × 5 × 8

A = 40cm2

Hence, the area of rhombus is 40cm2.

Question 3: If a square has its one side 20cm. What will be its perimeter and area?

Solution:

Given,

Side of square = 20cm

Now,

Perimeter of square(P) = 4(side)

P = 4 × 20

P = 80cm

Then, 

Area of square(A) = (side)2

A = 20 × 20 

A = 400cm2

Hence, the perimeter of a square is 80cm and its area is 400cm2.

Question: Find the volume of a cuboid having length 10cm, breadth 4cm, and height 5cm.

Solution:

Length(l) = 10cm

Breadth(b) = 4cm

Height (h) = 5cm

Now,

Volume of cuboid (V) = length × breadth × height

V = 10 × 4 × 5

V = 200cm3

Hence, the volume of cuboid is 200cm3.

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