Mensuration - Plane Figures

  A 2D shape is surrounded by 3 or more straight lines that can be represented on a plane surface.
      2D shapes have only length and breadth, and not height.
           For 2D shapes, area and perimeter are measuring parameters related to various two dimentional figures like triangle, rectangle, square etc.
Area
Total space enclosed by the boundary of plane figure is called the area of that particular figure.

    In another words, the area of figure is a measure associated with the part of plane enclosed in the figure.
       Area is measured in square unit like square metre, square centimetre etc.

Perimeter

Perimeter is the length of border around any enclosed plane figure.

   Therefore, sum of the sides of a plane figure is the perimeter of that particular figure. Unit of perimeter is same as the unit of side of the given figure.
Like metre, centimetre etc.

1. Find the perimeter of triangle with sides equals to 3 cm, 8 cm, 6 cm.
a) 14 cm              b) 15 cm            c) 17 cm
d) 18 cm             e) None
Sol: Perimeter = sum of sides
= 3 + 8 + 6 = 17 cm

Ans: c

2. If the side of square and its area are in the ratio of 1 : 11 then find its perimeter.
a) 48 cm        b) 40 cm            c) 44 cm
d) 50 cm        e) None

Sol: Let the side of square = a cm.
According to the question a : a² = 1 : 11
a = 11 cm
Side = 11 cm
Perimeter of square = 4 × side of square
Perimeter of square = 44 cm.
Ans: c
 

3. Numerically the side of square is 10% of its area then find the perimeter of square.
a) 40 cm             b) 44 cm                c) 48 cm
d) 52 cm                   e) None

Sol: Let the side of square = a cm.
a : a² = 1:10
a = 10 cm
Side = 10 cm
Perimeter of square = 4 × side of square
Perimeter of square = 40 cm

Ans: a
 

4. If the circumference of a circle is 176 cm then find the area of the circle.

a) 1464 cm²            b) 2264 cm²        c) 2474 cm²
d) 2464 cm²               e) None

Ans: d

5. If the perimeter of rectangle is 80 cm and its length is 2 cm more than breadth then find its area.
a) 324 cm²              b) 400 cm²
c) 399 cm²              d) 361 cm²                  e) None

Sol: According to the question.
Let the length and breadth of rectangle are
x cm and x – 2 cm respectively.
Perimeter of rectangle =
2 × (Length + Breadth)
2 (x + x − 2) = 80 x = 21 Length = x = 21 cm
Breadth = x − 2 = 19 cm
Area of rectangle = Length × Breadth
Area of rectangle = 21 × 19 = 399 cm²

Ans: c

6. If the area of rectangle is 160 cm2 and its length is 6 cm more than breadth then find its perimeter.
a) 52 cm            b) 26 cm             c) 50 cm
d) 80 cm              5) None

Ans: a

7. Numerically the circumference of circle is 40% of its area then what is the area of the circle?
a) 87.52 cm²              b) 64.52 cm²
c) 78.57 cm²              d) 75.21 cm²              e) None

Ans: c

8. Numerically the perimeter of square is th of its area then find the length of its diagonal.

Ans: d

9. If the area of square is 256 cm2 then find the length of its diagonal.

Ans: a

10. If the diagonal of square is then find its perimeter.

a) 37.5 cm         b) 25 cm           c) 50 cm
d) 62.5 cm           e) None

Ans: c

11. If the diagonal of a square is then find the maximum circumference of a circle that can be inscribed in the square.

a) 61.50 cm              b) 31.43 cm           c) 86.25 cm

d) Cannot be determined             e) None

Ans: b

12. Find the area of a rectangle whose length is 10 cm and breadth is equal to the side of a square whose area is 64 cm²

a) 125 cm²          b) 120 cm²             c) 80 cm²

d) 78 cm²          e) None

Sol: Length of rectangle = 10 cm
Area of rectangle = [Length × Breadth] ........(1)
Area of square = 64 cm²
Area of square = (Side)2 = 64 cm²
Side of square = 8 cm
Breadth of rectangle = Side of square ........(2)
Breadth of rectangle = 8 cm
Area of rectangle = 10 × 8 = 80 cm²

Ans: c