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Mathematics (Perimeter and Area)

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Ujjal Sharma
Ujjal Sharma

The document provides information on perimeter and area of different shapes like rectangle, square, parallelogram, triangle, and circle. It defines each shape and provides formulae to calculate perimeter and area. It then gives examples of calculating perimeter and area of these shapes by applying the formulae. It also includes some word problems involving calculation of perimeter and area of fields, wheels, etc.

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Mathematics (Perimeter and Area)
Introduction Formulae Solving sums HOT Questions
P e r i me t e r : P e r i me t e r i s t h e d i s t a n c e a r o u n d a 2D s h a p e . L i k e i n t h e f o l l o wi n g s h a p e t h e d i s t a n c e o f t h e b o r d e r o r t h e s h a d e d p o r t i o n i s t h e Pe r i me t e r .
Ar e a : A r e a i s t h e i n n e r s u r f a c e o f a s h a p e o r t h i n g , i t i s u s u a l l y a 2D s h a p e . L i k e i n t h e f o l l o wi n g s h a p e t h e s h a d e d p o r t i o n i s Area t h e Ar e a o f t h e s h a p e .
I n t h i s p r e s e n t a t i o n we wi l l l e a r n a b o u t t h e f o l l o w i n g sPhea rp ie m : t e s e r i s 1. R e c t a n g l e a l wa y s 2.S q u a r e e x p r e s s e 3.P a r a l l e l o gdr ai m U n i t n 4.T r i a n g l e a n d a r e a 5.C i r c l e i n U n i t 2. We w i l l l e a r n a b o u t t h e a r e a a n d p e r i me t e r .
Re c t a Re c t a n g l e P e r i me t en : l e r g me a n s m e a n s , L +B +L +B f o u r 5 cm s i d e s h a p e wh i c h 2 cm 2 cm h a s o p p o s i t e Perimeter is 2 x (5+2) = 14 cm 5 cm s i d e s e q u a l . Ar e a : 5 cm Area is 5 x 2 2 cm 2 cm = 10 cm2 5 cm
Sq u a r e Sq u a r e i s a P e r i me t e r : , me a snh s p e a S +S +S +S . l i k e r e c t a n g 2 cm l e wh i c h Perimeter is 4 x 2 h a s a l l 2 cm 2 cm s i d e s = 8 cm e q u a l . 2 cm 2 cm Ar e a : 2 cm 2 cm Area is 2 x 2 = 4 cm2 2 cm
P a r a l l e l o g r aA m a l p a r l e P e r i me t e r : l o g r a m i s a , m e a n 5 s S +B +S +B . cm s h a p e wh i c h h a s o p p o s i t 3 cm 3 cm e s i d e s p a r a l l e Perimeter is l a n d 5 cm e q u a l . 2 x (5+3) = 16 cm 5 cm Ar e a : 3 cm Area is 5 x 3 = 15 cm2 Altitude 5 cm
Tr i a n g l e I t s h i s a a p e wh i c h h a s P e r i me t e r : 3 s i d e s c l o s e d .(i t i s h a l f o f a 3 cm 4 cm a p r a l l e l o Perimeter is g r a m. 3+4+2 = 9 cm 2 cm Ar e a : 3 cm Area is 遜 x 4 x 3 = 6 cm2 4 cm
Ci r c l e i s a Ci r c l e s h a p e wh i c h h a s P e r i me t e r : n o e d g e a n d h a s a Ce n t r e p o i n t , d i a me t e r , Perimeter is r a d i u s (h a l 4 cm f o f 3.14 x 4 = 12.56 cm d i a m e t e r ), e t c . Ar e a : 3 cm Area is 3.14 x 32
A rectangular field is 45 m long 20 m wide, a person ran around it. How much did he run? Length of the field = 45 m Breadth of the field = 20 m Therefore, Perimeter = 2 (45+20) m = 2 x 65 m = 130 m Ans: He covered 130 m A rectangular field is 10 m long and 7 m wide. What is the area of the field? Length of the field = 10 m Breadth of the field = 7 m Therefore, Area = 10 x 7 m 2 = 70 m2 Ans: The area is 70 m 2 .
Find the perimeter of the square which has the sides of 2 cm. Side of the square = 25 cm Therefore the perimeter = 25 x 4 = 100 cm Ans: The perimeter is 100 cm. Find the area of the square which has the side of 7 cm. Side of the square = 7 cm Area of the square = 7 x 7 cm 2 = 49 cm2 Ans: The area is 49 cm2
Find the perimeter of a parallelogram which has the sides of 15 and 10 cm. Parallel sides of the parallelogram = 15 cm Parallel sides of the parallelogram = 10 cm Therefore, perimeter = 2 x (10+15) = 2 x 25 = 50 cm Ans: The perimeter is 50 cm. Find the area of a parallelogram which has altitude of 14 cm and base of 20 cm. Altitude of the parallelogram = 14 cm Base of the parallelogram = 20 cm Therefore area = 14 x 20 = 280 cm 2 Ans: Area of the parallelogram is 280 cm2
An equilateral triangle has sides of 36 cm. A person rolled around a wire around it. What is the length of the wire? Length of the side of the equilateral triangle = 36 cm Therefore, perimeter = 36 x 3 = 108 cm Ans: The length of the wire is 108 cm. A triangle has a base of 10 cm and has the altitude of 15 cm. Find the area of the triangle. Base of the triangle = 10 cm Altitude of the triangle = 15 cm Therefore, Area = 遜 x 10 x 15 = 75 cm 2 Ans: The area is 75 cm 2.
Amit has a circular disc. He measured the radius which is 8 cm. What is the circumference of the circle. Diameter of the circle = 8 x 2 = 16 cm Therefore, perimeter is 3.14 x 16 = 50.24 cm Ans: The circumference is 50.24 cm. Rajan has a wheel which has diameter of 10 cm. He wants cover it with a flat cover. For that he needs to find the area. What is the area? Radius of the wheel = 10/2 = 5 cm Therefore, area = 3.14 x 5 x 5 = 78.5 cm 2 Ans: The area is 78.5 cm 2
A man wants to fence around this shaped field. His brother wants put grass in that field. Cost of the fencing is Rs. 10 / m and cost of putting grass is Rs. 7 / m 2 . Which costs more? Fencing: Perimeter is 2+7+7+4+10 cm = 30 cm 7m Therefore, the cost is Rs. 30 x 10 = Rs 300 is cost of fencing. Putting grass: Area of the square 7x 7 7m 4m = 49 m2 Area of the rectangle 4 by 3 m 10 m = 4 x 3 = 12 m 2 Area of the triangle = 遜 x 3 x 3 = 4.5 m 2 Total area is 49+12+4.5 m 2 = 65.5 m2 Cost is Rs. 7 x 65.5 = Rs. 458.5 Ans: Putting grass is more costly.
A square has a same area of a triangle. The side of the square is x, and base of the triangle is also x, what will be the altitude of the triangle? The area of the triangle = xxx Therefore, let the altitude be a ATQ X x a x 遜 = x2 a x 遜 = x2 / x a=xx2 a = 2x Ans: the altitude is 2x
A parallelogram has a altitude of 10 cm . And a circle has a area of equal to the area of the parallelogram. The circle also has the diameter of 10 cm. find the base of the parallelogram. Area of the parallelogram = Area of the Circle Therefore, Area of the circle = 3.14 x r x r Radius = 10/2 = 5 cm Therefore area = 3.14 x 5 x 5 = 3.14 x 25 = 78.5 cm 2 Therefore base of the parallelogram = 78.5/10 = 7.85 cm Ans: The base is 7.85 cm
Mathematics (Perimeter and Area)

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Mathematics (Perimeter and Area)

  • 2. Introduction Formulae Solving sums HOT Questions
  • 3. P e r i me t e r : P e r i me t e r i s t h e d i s t a n c e a r o u n d a 2D s h a p e . L i k e i n t h e f o l l o wi n g s h a p e t h e d i s t a n c e o f t h e b o r d e r o r t h e s h a d e d p o r t i o n i s t h e Pe r i me t e r .
  • 4. Ar e a : A r e a i s t h e i n n e r s u r f a c e o f a s h a p e o r t h i n g , i t i s u s u a l l y a 2D s h a p e . L i k e i n t h e f o l l o wi n g s h a p e t h e s h a d e d p o r t i o n i s Area t h e Ar e a o f t h e s h a p e .
  • 5. I n t h i s p r e s e n t a t i o n we wi l l l e a r n a b o u t t h e f o l l o w i n g sPhea rp ie m : t e s e r i s 1. R e c t a n g l e a l wa y s 2.S q u a r e e x p r e s s e 3.P a r a l l e l o gdr ai m U n i t n 4.T r i a n g l e a n d a r e a 5.C i r c l e i n U n i t 2. We w i l l l e a r n a b o u t t h e a r e a a n d p e r i me t e r .
  • 6. Re c t a Re c t a n g l e P e r i me t en : l e r g me a n s m e a n s , L +B +L +B f o u r 5 cm s i d e s h a p e wh i c h 2 cm 2 cm h a s o p p o s i t e Perimeter is 2 x (5+2) = 14 cm 5 cm s i d e s e q u a l . Ar e a : 5 cm Area is 5 x 2 2 cm 2 cm = 10 cm2 5 cm
  • 7. Sq u a r e Sq u a r e i s a P e r i me t e r : , me a snh s p e a S +S +S +S . l i k e r e c t a n g 2 cm l e wh i c h Perimeter is 4 x 2 h a s a l l 2 cm 2 cm s i d e s = 8 cm e q u a l . 2 cm 2 cm Ar e a : 2 cm 2 cm Area is 2 x 2 = 4 cm2 2 cm
  • 8. P a r a l l e l o g r aA m a l p a r l e P e r i me t e r : l o g r a m i s a , m e a n 5 s S +B +S +B . cm s h a p e wh i c h h a s o p p o s i t 3 cm 3 cm e s i d e s p a r a l l e Perimeter is l a n d 5 cm e q u a l . 2 x (5+3) = 16 cm 5 cm Ar e a : 3 cm Area is 5 x 3 = 15 cm2 Altitude 5 cm
  • 9. Tr i a n g l e I t s h i s a a p e wh i c h h a s P e r i me t e r : 3 s i d e s c l o s e d .(i t i s h a l f o f a 3 cm 4 cm a p r a l l e l o Perimeter is g r a m. 3+4+2 = 9 cm 2 cm Ar e a : 3 cm Area is 遜 x 4 x 3 = 6 cm2 4 cm
  • 10. Ci r c l e i s a Ci r c l e s h a p e wh i c h h a s P e r i me t e r : n o e d g e a n d h a s a Ce n t r e p o i n t , d i a me t e r , Perimeter is r a d i u s (h a l 4 cm f o f 3.14 x 4 = 12.56 cm d i a m e t e r ), e t c . Ar e a : 3 cm Area is 3.14 x 32
  • 11. A rectangular field is 45 m long 20 m wide, a person ran around it. How much did he run? Length of the field = 45 m Breadth of the field = 20 m Therefore, Perimeter = 2 (45+20) m = 2 x 65 m = 130 m Ans: He covered 130 m A rectangular field is 10 m long and 7 m wide. What is the area of the field? Length of the field = 10 m Breadth of the field = 7 m Therefore, Area = 10 x 7 m 2 = 70 m2 Ans: The area is 70 m 2 .
  • 12. Find the perimeter of the square which has the sides of 2 cm. Side of the square = 25 cm Therefore the perimeter = 25 x 4 = 100 cm Ans: The perimeter is 100 cm. Find the area of the square which has the side of 7 cm. Side of the square = 7 cm Area of the square = 7 x 7 cm 2 = 49 cm2 Ans: The area is 49 cm2
  • 13. Find the perimeter of a parallelogram which has the sides of 15 and 10 cm. Parallel sides of the parallelogram = 15 cm Parallel sides of the parallelogram = 10 cm Therefore, perimeter = 2 x (10+15) = 2 x 25 = 50 cm Ans: The perimeter is 50 cm. Find the area of a parallelogram which has altitude of 14 cm and base of 20 cm. Altitude of the parallelogram = 14 cm Base of the parallelogram = 20 cm Therefore area = 14 x 20 = 280 cm 2 Ans: Area of the parallelogram is 280 cm2
  • 14. An equilateral triangle has sides of 36 cm. A person rolled around a wire around it. What is the length of the wire? Length of the side of the equilateral triangle = 36 cm Therefore, perimeter = 36 x 3 = 108 cm Ans: The length of the wire is 108 cm. A triangle has a base of 10 cm and has the altitude of 15 cm. Find the area of the triangle. Base of the triangle = 10 cm Altitude of the triangle = 15 cm Therefore, Area = 遜 x 10 x 15 = 75 cm 2 Ans: The area is 75 cm 2.
  • 15. Amit has a circular disc. He measured the radius which is 8 cm. What is the circumference of the circle. Diameter of the circle = 8 x 2 = 16 cm Therefore, perimeter is 3.14 x 16 = 50.24 cm Ans: The circumference is 50.24 cm. Rajan has a wheel which has diameter of 10 cm. He wants cover it with a flat cover. For that he needs to find the area. What is the area? Radius of the wheel = 10/2 = 5 cm Therefore, area = 3.14 x 5 x 5 = 78.5 cm 2 Ans: The area is 78.5 cm 2
  • 16. A man wants to fence around this shaped field. His brother wants put grass in that field. Cost of the fencing is Rs. 10 / m and cost of putting grass is Rs. 7 / m 2 . Which costs more? Fencing: Perimeter is 2+7+7+4+10 cm = 30 cm 7m Therefore, the cost is Rs. 30 x 10 = Rs 300 is cost of fencing. Putting grass: Area of the square 7x 7 7m 4m = 49 m2 Area of the rectangle 4 by 3 m 10 m = 4 x 3 = 12 m 2 Area of the triangle = 遜 x 3 x 3 = 4.5 m 2 Total area is 49+12+4.5 m 2 = 65.5 m2 Cost is Rs. 7 x 65.5 = Rs. 458.5 Ans: Putting grass is more costly.
  • 17. A square has a same area of a triangle. The side of the square is x, and base of the triangle is also x, what will be the altitude of the triangle? The area of the triangle = xxx Therefore, let the altitude be a ATQ X x a x 遜 = x2 a x 遜 = x2 / x a=xx2 a = 2x Ans: the altitude is 2x
  • 18. A parallelogram has a altitude of 10 cm . And a circle has a area of equal to the area of the parallelogram. The circle also has the diameter of 10 cm. find the base of the parallelogram. Area of the parallelogram = Area of the Circle Therefore, Area of the circle = 3.14 x r x r Radius = 10/2 = 5 cm Therefore area = 3.14 x 5 x 5 = 3.14 x 25 = 78.5 cm 2 Therefore base of the parallelogram = 78.5/10 = 7.85 cm Ans: The base is 7.85 cm