Area of Plane Figures
Subject: Compulsory Maths
Overview
The plane surface enclosed by the boundary line of a plane closed figure is known as its area . The area is always measured in the square unit. For example,cm2 , mm2,m2etc . This note gives information about different solid figure and also its formula.Area of Plane Figures
The plane surface enclosed by the boundary line of a plane closed figure is known as its area . The area is always measured in a square unit. For example,cm2 , mm2,m2etc.
Area of rectangles :
In the adjoining graph , the area of each square room is 1 cm2. So , the surface enclosed by the rectangle is 10 cm2.
\(\therefore\) Area of rectangle = 10 cm2
i.e . 5 rooms along length x 2 rooms breadth = 10cm2
\(\therefore\) Area of rectangle = length x breadth = l x b
Area of triangles
Here , area of the triangle EFG= length x breadth
=FG xGH
=base x height
=b x\(\frac{1}{2}\)h
\(\frac{1}{2}\)bh
So the area of triangle =\(\frac{1}{2}\)base x height = \(\frac{1}{2}\)b xh
Area of trianglesgle
Here , area of triangle = area of rectangle FGHI
= length x breadth
=FG XGH
=base x hieight
=b x\(\frac{1}{2}\)
=\(\frac{1}{2}\)bh
So , the area of tringle =\(\frac{1}{2}\)base x height = \(\frac{1}{2}\) b xh
Area of Parallelogrms
Here , area of the parallelogram EFGH =Area of the rectangle of EFGH
= length x breadth
=EF x FI
= base x height
= b x h
So, the area of parallelogram = base x height
= b x h
Area of circles :
The length of rectangle EFGH (l) =\(\frac{1}{2}\) x circumference = \(\frac{1}{2}\) x2 πr
The breadth of rectangle EFGH (b) = r
area of the circle = Area of rectangle EFGH
= length x breadth
=πr x r
=πr2
So , the area of circle =πr2
Things to remember
- Area of rectangle = length x breadth = l x b.
- The area of parallelogram = base x height.
- The area of circle =πr2
- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.
Videos for Area of Plane Figures
Areas of Plane Figures
Perimeter and Area- Plane figures - Maths - Class 7
Questions and Answers
Find the area of the given figure.
Solution:
Here,
area of two rectangles = l × b
= 20 cm × 15 cm
= 300 cm2
Also,
area of two triangles = 2 (\(\frac{1}{2}\) ×b × h)
= 2 × \(\frac{1}{2}\) × 15 × 10 cm2
= 150 cm2
Again,
∴ Area of the figure = 300 cm2 + 150 cm2
= 450 cm2
Find the area of the given figure.
Solution:
Area of the rectangle = l × b
= 20 cm × 15 cm
= 300 cm2
Radius of each semi-circle = \(\frac{14}{2}\)
= 7 cm
Area of two semi-circles = 2(\(\frac{1}{2}\)πr2)
= \(\frac{22}{7}\) × 7 × 7 cm2
= 154 cm2
∴ Area of the figure = 350 cm2 + 154 cm2
= 504 cm2
Find the area of the shaded region in the given figure.
Solution:
Here,
Area of parallelogram = b × h
= 16 cm × 10cm
= 160 cm2
Area of triangle = \(\frac{1}{2}\) b × h
= \(\frac{1}{2}\) × 16 cm × 10 cm
= 80 cm2
∴ Area of the shaded region = Area of parallelogram -Area of triangle
= 160 cm2 - 80 cm2
= 80 cm2
Find the area of the shaded regions in the given figures.
Solution:
Area of rectangle = l × b
= 12 cm × 9 cm
= 108 cm2
Area of parallelogram = b × h
= 6 cm × 4 cm
= 24 cm2
∴ Area of the shaded region = Area of rectangle - Area of parallelogram
= 108 cm2 - 24 cm2
= 84 cm2
Find the area of shaded regions in the given figure.
Solution:
Here,
Area of bigger rectangle = l × b
= 20 cm × 16 cm
= 320 cm2
Area of smaller rectangle = l × b
= 14 cm × 10 cm
= 140cm2
∴ Area of the shaded region = Area of bigger recatngle - Area of smaller rectangle
= 320 cm2 - 140 cm2
= 180 cm2
The perimeter of a square field is 96 m. Find its length.
Solution:
The perimeter of the square field = 96 m
or, 4 l = 96 m
or, l = \(\frac{96}{4}\)
or, l = 24 m
∴ The length of the field (l) = 24m
A rectangular room is twice as long as its breadth and its perimeter is 48 m. Find its length and breadth and area.
Solution:
Let, the breadth (b) pf the room be x m.
So, the length (l) of the room will be 2x m.
Now,
The perimeter of the rectangular room = 48 m
or, 2 (l + b) = 48 m
or, 2 (2x + x) = 48 m
or, 6x = 48 m
or, x = \(\frac{48}{6}\) m
or, x = 8 m
∴ The breadth of the room (b) = x = 8 m
The length of the room (l) = 2x
= 2 × 8m
= 16 m
Again.
Area of the room = l × b
= 16 m × 8 m
= 128 m2
∴ Thw area of a room is 128 m2
If the perimeter of a circular ground is 220 m, find its radius and area.
Solution:
Here,
The perimeter of circular ground = 220 m
or, 2πr = 220 m
or, 2 × \(\frac{22}{7}\) × r = 220 m
or, r = \(\frac{220 × 7}{2 × 22}\) m
or, r = 35 m
Now,
Area of the circular ground = πr2
= \(\frac{22}{7}\) × 35 m × 35 m
= 3850 m2
Quiz
© 2019-20 Kullabs. All Rights Reserved.