In the figure (ii) given below, ABC is an equilateral triangle of side 8 cm. A, B and C are the centers of circular arcs of equal radius. Find the area of the shaded region correct upto 2 decimal places.

We know that △ABC is an equilateral triangle of side 8 cm A, B, C are the centres of three circular arcs of equal radius Radius = = 4 cm By formula, Area of △ABC = = × 8 × 8 = = = 16 × 1.732 = 27.712 cm 2 . So, the area of 3 equal sectors of 60° whose radius is 4 cm = 3 × πr 2 × = 3 × 3.142 × 4 × 4 × = 3.142 × 8 = 25.136 cm 2 . Area of shaded region = Area of equilateral triangle - Area of 3 sectors = 27.712 – 25.136 = 2.576 ≈ 2.58 cm 2 . Hence, area of shaded region = 2.58 cm 2 .

In the adjoining figure, a chord AB of a circle of radius 10 cm subtends a right angle at the centre O. Find the area of the sector OACB and of the major segment. Take π = 3.14.

View Answer Bookmark Now

In the figure (ii) given below, a piece of cardboard, in the shape of a trapezium ABCD and AB || CD and ∠BCD = 90°, quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2 cm. Calculate the area of the remaining piece of the cardboard.

View Answer Bookmark Now

In the figure (i) given below, ABC is a right angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semi-circle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.

View Answer Bookmark Now

Mathematics

In the figure (ii) given below, ABC is an equilateral triangle of side 8 cm. A, B and C are the centers of circular arcs of equal radius. Find the area of the shaded region correct upto 2 decimal places.

Mensuration

Related Questions

In the adjoining figure, a chord AB of a circle of radius 10 cm subtends a right angle at the centre O. Find the area of the sector OACB and of the major segment. Take π = 3.14.

In the figure (ii) given below, a piece of cardboard, in the shape of a trapezium ABCD and AB || CD and ∠BCD = 90°, quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2 cm. Calculate the area of the remaining piece of the cardboard.

In the figure (i) given below, ABC is a right angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semi-circle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.