Introduction for plane geometry practice:
In this branch of mathematics,we study to measure a line segment, find the area of a plane surface and perimeter and the volume of solids.Proper units are chosen for different measurements. In this chapter we will derive standard formula for calculating area of the rectangle, the perimeter of a rectangle,the area of a square of a geometry practice problem.
Area and perimeter of plane geometry practice:
Area of a rectangle = length × breadth
A = l × b
perimeter of a rectangle = 2 lengths + 2 breadths
P = 2l + 2b
Area of a square = side × side
A = a2
Perimeter of a square = 4 × side
P = 4a
Examples for plane geometry practice problems:
Example 1:
Find (a) area and (b) perimeter of a square whose sides is 15 cm.
Solution :
(a) Side of the square, a = 15 cm
Area of the square, A = a2
= a × a
= 15 × 15
= 225 sq.cm (or 225 cm2)
(b) Perimeter of the square, P = 4a
= 4 × 15 cm
= 60 cm
Example 2:
Find the area and perimeter of a rectangle whose length is 4m and breadth is 50 cm.
Solution :
Length of the rectangle, l = 4 m or 400 cm
Breadth of the rectangle, b = 50 cm
(a) Area of the rectangle, A = l × b
= 400 cm × 50 cm
? Area = 20,000 sq.cm.
(b) Perimeter of the rectangle, P = 2l + 2b
= 2 × 400 cm + 2 × 50 cm
= 800 cm + 100 cm
? Perimeter = 1,000 cm
Example 3 :
The perimeter of the floor of a rectangular hall is 24 m. Its rectangle length is 9 meter. Find its area of rectangle.
Note : To find area we should know the measurements of length and breadths. Here rectangle length is given.
Hence we should find the breadths from the perimeter.
Solution :
2 length + 2 breadth = perimeter
2 × 9 + 2b = 24
18 + 2b = 24
2b = 24 – 18
2 b = 6
b =6/2 = 3
Now the area of the rectangle A = l b
= 9 m × 3 m
= 21 sq.m.
I have recently faced lot of problem while learning Pentagonal Prism Volume Formula, But thank to online resources of math which helped me to learn myself easily on net.
Practice problem for plane geometry :
Find the cost of fencing a rectangular park of lengths 170 m and breadth 100 m at the rate of Rs.9 per metre.
Answer:Rs.2800
In this branch of mathematics,we study to measure a line segment, find the area of a plane surface and perimeter and the volume of solids.Proper units are chosen for different measurements. In this chapter we will derive standard formula for calculating area of the rectangle, the perimeter of a rectangle,the area of a square of a geometry practice problem.
Area and perimeter of plane geometry practice:
Area of a rectangle = length × breadth
A = l × b
perimeter of a rectangle = 2 lengths + 2 breadths
P = 2l + 2b
Area of a square = side × side
A = a2
Perimeter of a square = 4 × side
P = 4a
Examples for plane geometry practice problems:
Example 1:
Find (a) area and (b) perimeter of a square whose sides is 15 cm.
Solution :
(a) Side of the square, a = 15 cm
Area of the square, A = a2
= a × a
= 15 × 15
= 225 sq.cm (or 225 cm2)
(b) Perimeter of the square, P = 4a
= 4 × 15 cm
= 60 cm
Example 2:
Find the area and perimeter of a rectangle whose length is 4m and breadth is 50 cm.
Solution :
Length of the rectangle, l = 4 m or 400 cm
Breadth of the rectangle, b = 50 cm
(a) Area of the rectangle, A = l × b
= 400 cm × 50 cm
? Area = 20,000 sq.cm.
(b) Perimeter of the rectangle, P = 2l + 2b
= 2 × 400 cm + 2 × 50 cm
= 800 cm + 100 cm
? Perimeter = 1,000 cm
Example 3 :
The perimeter of the floor of a rectangular hall is 24 m. Its rectangle length is 9 meter. Find its area of rectangle.
Note : To find area we should know the measurements of length and breadths. Here rectangle length is given.
Hence we should find the breadths from the perimeter.
Solution :
2 length + 2 breadth = perimeter
2 × 9 + 2b = 24
18 + 2b = 24
2b = 24 – 18
2 b = 6
b =6/2 = 3
Now the area of the rectangle A = l b
= 9 m × 3 m
= 21 sq.m.
I have recently faced lot of problem while learning Pentagonal Prism Volume Formula, But thank to online resources of math which helped me to learn myself easily on net.
Practice problem for plane geometry :
Find the cost of fencing a rectangular park of lengths 170 m and breadth 100 m at the rate of Rs.9 per metre.
Answer:Rs.2800
