Question

a shape of a garden is rectangular in the middle and semi circuler at the end as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20-(3.5+3.5)meters]​

Answer 1

Answer:

Perimeter of garden = 48 m

Area of garden = 129.5 m²

Step-by-step explanation:

General Instruction:-

This type of shape called plane shape. This shape is made of 2 semi - circles and one rectangle.

Given :-

Length of the garden = 20 m

Breadth of the rectangle = 7 m

Diameter of circle = 7 m  (Breadth of rectangle = Diameter of circle)

we know that radius is a 1/2 of its diameter so,

Radius of a circle = 7/2 m

                            = 3.5 m

So,

Length of rectangle = 20 -(3.5 + 3.5) m     (Given in question)

                                 = 20 - 7 m

                                 = 13 m.

we find circumference of 1st circle......

so, circumference of 1st circle = πr      (we know the value of π = 22/7)

=> 22/7 * 3.5 m

=> 22 * 0.5 m

=> 11 m

Similarly circumference of 2nd circle = 11 m

So, circumference of both the circle = 11 m + 11 m

                                                            = 22 m

So, Perimeter of garden =  AB + CD + circumference of 2 circles  

we know all the value so we put the value in this

=> 13 + 13 + 22

=> 48 m

So, Perimeter of garden = 48 m

Now, Area of garden = Area of rectangle + area of 2 semi circle

So, we first find area of rectangle

Area of rectangle = l * b

=> 13 * 7

=> 91 m²

So, Area of rectangle = 91 m²

And secondly we find area of 2 semi circles = 2 * 1/2πr²

=> πr²

=> 22/7 * 3.5 * 3.5

=> 22 * 0.5 * 3.5

=> 38.5 m²

So, the area of 2 circumference of circle = 38.5 m²

Then we put the value in the formula.

Area of garden = Area of rectangle + area of 2 semi circle

=> 91 m² + 38.5 m²

=> 129.5 m²

So, Area of garden = 129.5 m²

Answer 2

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Total area of the garden = Area of the rectangular portion + The sum of the areas of the pair of semi-circles

$l.b + 2 \times \frac{1}{2}\pi {r}^{2}$

$= (13 \times 7) {m}^{2} +$

$(2 \times \frac{1}{2} \times \frac{22}{7} \times 3.5 \times 3.5) {m}^{2}$

$= (91 + 38.5) {m}^{2} = 129.5 {m}^{2}$

Perimeter of the garden =2× length of rectangular portion + circumference of the circle

$= (2 \times 13 + 2 \times \frac{22}{7} \times 3.5)m$

$= (26 + 22)m = 48m$