Notes on Area of Plane Figures | Grade 7 > Compulsory Maths > Perimeter, Area and Volume | KULLABS.COM

Area of Plane Figures

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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



  • Area of rectangle = length x breadth = l x b.
  • The area of parallelogram = base x height.
  • The area of circle =πr2
.

Very Short Questions

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

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 cm
= 504 cm2

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

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

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

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 

0%
  • The formula of area of rectangle is ______ .

    l × b
    l + b
    l ÷ b
    l - b
  • The formula of area of triangle is ______ .

    (frac{1}{2}) b × h
    b × h × l
    b × h
    l × b
  • The formula of area of parallelograms is ______.

    l × h
    l × b × h
    b × h
    l × b
  • If the perimeter of a circular ground is 220 m, then find its radius.

    36 m
    37 m
    35 m 
    34 m
  • Find the area of triangle in which base = 8 cm, height = 5.5 cm.

    22 cm2
    24 cm2
    21 cm2
    23 cm2
  • The perimeter of a square ground is 128 m, find its area.

    1036 m2
    1024 m2
    1012 m2
    1042 m2
  • Find the area of a square field is 625 m2,  find its perimeter.

    100m 
    70m
    80m
    90m
  • If the perimeter of a circle is 44cm, find its area.

    123 cm2
    154 cm2
    147 cm2
    138 cm2
  • A square room is 15 m long, what will be its area of carpet required to cover its floor.

    225 m2
    235 m2
    240 m2
    210 m2
  • A rectangular field is 40 m long and its area is 1120 m2, find its breadth.

    22 m 
    28 m
    20 m
    24 m 
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