Question

The shape of a garden is as shown in the pic. It is rectangular in the middle and semicircular at the ends. Find the area and perimeter of this garden.

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Answer 1

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

= l.b + 2× 1/2 πr ²

Mensuration:

Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.

Plane Figure: A figure which lies in a plane is called a plane figure.

For e.g:  a rectangle, square, a rhombus, a parallelogram, a trapezium.

 

Perimeter:

The perimeter of a closed plane figure is the total length of its boundary.

In case of a triangle or a polygon the perimeter is  the sum of the length of its sides.

Unit of perimeter is a centimetre  (cm), metre(m) kilometre(km) e.t.c

Area: The area of the plane figure is the measure of the surface enclose by its boundary.

 

The area of a triangle are a polygon is the measure of the surface enclosed by its sides.

A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.

Circumference of a circle is the perimeter of a circle.

In a circle the radius is half of the diameter.

The approximate value of π( Pi) is= 22/7 

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Answer 2

Answer:

QUESTION:-

The shape of a garden is as shown in the pic. It is rectangular in the middle and semicircular at the ends. Find the area and perimeter of this garden.

ANSWER :-

Area of the garden = 518 m²

Perimeter of the garden = 96 m

STEP BY STEP SOLUTION:-

length of the rectangle

➙ 40 m - r - r

➙ 40 m - 2r

➙ 40 m - 2 * 14/2m

➙ 26 m

Width of the rectangle

➙ 14 m

• Area of rectangle

➙26 m * 14 m

➙ 364 m²

Diameter of the semicircular ends

➙ 14 m

• Radius of the semicircular ends

➙ 14/2 = 7 m

Area of two semicircular ends

➙ 2 * πr²/2 = πr²

• Area of two semicircular ends

➙ πr²

➙ 22/7 * 7 * 7² = 154 m²

Area if garden = area of rectangle + Area of two semicircular ends

Area of garden = (364 + 154) m²

Area of garden = 518 m²

perimeter of garden = 2 * length of the rectangle + 2πr²

perimeter of garden

= ( 2 * 26 ) m + ( 2 * 22/7 * 7 ) m

= ( 52 + 44 ) m

➙ 96 m