Question

19th October, 2020

the diagram below is a plane figure made up
of a rectangle of sizes 50m by 28 m and an
equilateral of height 24 cm. A circle is cut-out
of the rectangle as shown. If the circle
touches the three sides of the rectangle Calculate
a) the perimeter of the figure
the remaining portion of the figure.
​

Answer 1

Explanation:

Equilateral Triangle:

Side of triangle = breadth of rectangle

= 28 cm

height = 24 cm

Area of triangle =
`(1)/(2)base * height\\\\`

=
`(1)/(2)*28*24`

= 28* 12

= 336 square cm

Rectangle:

length = 50 m

breadth = 28 m

Area of rectangle = length * breadth

= 28 * 50

= 1400 square cm

Diameter of circle = breadth of rectangle

d = 28 cm

r = 28/2 = 14 cm

Area of circle = πr²

`= (22)/(7)*14*14\\\\= 22 * 2 * 14`

= 616 square cm

Area of the remaining portion = Area of rectangle - area of circle + area of triangle

= 1400 - 616 + 336

= 1120 square cm

Perimeter of the figure = 28 + 50 + 28 + 28 + 50

= 184 cm

Hint: Perimeter of the figure. three side of rectangle + two sides of triangle