Question

Find the area of the following shape, given its curves are made from parts of circles with diameters indicated on the diagram Give your answers in terms of pi.​

Answer 1

QUESTION: Find the area of the following shape, given its curves are made from parts of circles with diameters indicated on the diagram Give your answers in terms of pi.​

GIVEN:

2*big semi-circle with radius 5cm

2*Small semi-circle with radius 1 cm

1*Rectangle length=10cm,breadth=2cm

TO FIND:

The area of the shape

SOLUTION:

For the first two big semi-circles, they combine to form a complete circle

$AREA=\pi R^{2} \\AREA=\pi 5^{2} \\AREA=25\pi cm^{2}$

For the second two semi-circles, they combine to form a complete circle

$AREA=\pi R^{2} \\AREA=\pi 1^{2} \\AREA=\pi cm^{2}$

For the area of the rectangle

$AREA=LENGTH*BREADTH\\AREA=10*2\\AREA=20cm^{2}$

The total area of complete shape=area of two big semi-circles + area of two small semi-circles + area of the rectangle

$=25\pi cm^{2} +\pi cm^{2} +20cm^{2}\\=(26\pi +20cm)^{2}$

HENCE, the area of the shape in terms of pie$=(26\pi +20cm^{2})$