Question

An equable shape is a shape that has the same numerical perimeter and area,
NOTE: (i) The figures are NOT TO SCALE. (ii) Lengths in figures are given in centimeters.
Question 11
Which one of the following is an equable shape? Choose the correct option
a) Figure A
b) Figure B
c) Both Figure A and B
d) Neither Figure A and B
3.6
4. S​

Answer 1

Given:

Attached figure with measurements in terms of centimetres

To find:

Which of the given figures is an equable in shape?

Solution:

Formula to used:

•  Area of a rectangle = length × breadth
• Area of a triangle = ½ × base × height
• Perimeter = sum of all sides

 

 

Since we are given that the an equable shape is a shape which has same perimeter and area, so we will find the area and perimeter of each of the given figures and check if it is same.

Figure (A):

Length = 3.6 cm

Breadth = 4.5 cm

∴ Area of a rectangle = 3.6 × 4.5 = 16.2 cm²

∴ Perimeter of a rectangle = 3.6 + 3.6 + 4.5 + 4.5 = 2 × [3.6 + 4.5] = 16.2 cm²

The figure A has its numerical area and perimeter same.

Figure (B):

Base = 3 + 3 = 6 cm

Height = 4 cm

∴ Area of a triangle =  ½ × 6 × 4 = 12 cm²

∴ Perimeter of a triangle = 6 + 6 + 6 = 18 cm²

For figure B the numerical area and perimeter are not the same.

Thus, the final answer is option (a) Figure A

 

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