Perimeter Of Rectangle With Semicircle

Area and Perimeter of a Semicircle

Here nosotros will discuss nigh the expanse and perimeter of a semicircle with some case problems.

Area of a semicircle = \(\frac{i}{ii}\) πr\(^{2}\)

Perimeter of a semicircle = (π + ii)r

Solved example bug on finding the area and perimeter of a semicircle:

1. Find the expanse and perimeter of a semicircle of radius 7 cm. (Apply π = \(\frac{22}{vii}\)).

Solution:

Given, radius = r = seven cm.

Then, area of semicircle = \(\frac{i}{ii}\) πr\(^{two}\)

                                   = \(\frac{ane}{ii}\) × \(\frac{22}{7}\) × vii\(^{2}\) cm\(^{2}\)

                                   = 11 × 7 cm\(^{2}\)

                                   = 77 cm\(^{2}\)

Perimeter of a semicircle = (π + 2)r

                                     = (\(\frac{22}{7}\) + 2) × 7 cm

                                     = \(\frac{36}{seven}\) × 7 cm

                                     = 36 cm

2. Find the area and perimeter of the figure in which PQRS is a square of side 28 cm and STR is a semicircle. (Use π = \(\frac{22}{seven}\)).

Solution:

The required area = Expanse of the square PQRS + Area of the semicircle STR

                          = a\(^{2}\) + \(\frac{1}{2}\) πr\(^{2}\)

                          = 28\(^{two}\) cm\(^{ii}\) + \(\frac{1}{2}\) × π × (\(\frac{1}{two}\) × 28)\(^{2}\) cm\(^{2}\)

                          = (28\(^{2}\) + \(\frac{1}{two}\) × \(\frac{22}{7}\) × 14\(^{2}\)) cm\(^{2}\)

                          = (28\(^{2}\) + \(\frac{1}{2}\) × \(\frac{22}{7}\) × 14 × xiv) cm\(^{2}\)

                          = (28\(^{ii}\) + xi × ii × 14) cm\(^{ii}\)

                          = (28\(^{2}\) + eleven × 28) cm\(^{2}\)

                          = 28(28 + eleven) cm\(^{2}\)

                          = 28 × 39 cm\(^{two}\)

                          = 1092 cm\(^{two}\)

The required perimeter = PQ + PS + QR + semicircular arc STR

                                  = 28 cm + 28 cm + 28 cm + π × (\(\frac{1}{2}\) SR)

                                  = 84 cm + \(\frac{22}{vii}\) × \(\frac{1}{2}\) × 28 cm

                                  = 84 cm + 11 × 4 cm

                                  = 84 cm + 44 cm

                                  = 128 cm

9th Course Math

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