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



(A) (b)​

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:

$\boxed{Area\: of\: a\: rectangle \:=\:length\:*\:breadth}$

$\boxed{Area\:of \:a\:triangle\:=\:\frac{1}{2}\:*\:base\:*\:height }$

$\boxed{Perimeter\:=\:sum\:of\:all\:sides}$

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 = $\frac{1}{2}$ × 6 × 4 = 12 cm²

We have, the length of one of two sides of the triangle = $\sqrt{4^2 + 3^2}$ = $\sqrt{25}$ = 5 cm

∴ Perimeter of the triangle = 5 + 5 + 6 = 16 cm²

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

Thus, the final answer is $\boxed{option\:(a)\::\:Figure\:A\:is\:an\:equable\:shape}$

------------------------------------------------------------------------------------------

Also View:

Which one is an equable shape. both 11q and 12q?

https://brainly.in/question/16917424

Answer 2

The correct option is a) Figure A

Step-by-step explanation:

The image given in the question is attached below.

A shape is said to be equable shape when the perimeter and area are equal.

Figure A is rectangle:

Area of rectangle is given by the formula:

A = l × b

On substituting the values, we get,

∴ A = 3.6 × 4.5 = 16.2 units²

Perimeter of rectangle is given by the formula:

P = 2(l + b)

On substituting the values, we get,

∴ P = 2(3.6 + 4.5) = 2(8.1) = 16.2 units

Since, Area = Perimeter. Thus, rectangle is a equable shape.

Figure B is triangle:

Area of triangle is given by the formula:

A = 1/2 × h × b

On substituting the values, we get,

∴ A = 1/2 × 3 × 6 = 9 units

Perimeter of triangle is given by the formula:

P = Sum of all sides

On substituting the values, we get,

∴ P = 5 + 5 + 6 = 16 units

Since, Area ≠ Perimeter. Thus, triangle is not a equable shape.