Q. 104.1( 186 Votes )

Answer :

Let the side of the equilateral triangle be *a*

Area of equilateral triangle = 17320.5 cm^{2}

(a)^{2} = 17320.5

(a)^{2} = 17320.5

a^{2} = 4 × 10000

a = 200 cm

Each sector is of measure 60° as each angle of an equilateral triangle is 60º.

Area of each sector = × π × r^{2}

= × π × (100)^{2}

=

= cm^{2}

Area of shaded region = Area of equilateral triangle - 3 × Area of each sector

= 17320.5 – 3 *

= 17320.5 – 15700

= 1620.5 cm^{2}

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSIn Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.NEXTOn a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

RELATED QUESTIONS :

If the total surface area of a solid hemisphere is 462 cm^{2}, find its volume. [Take π = 22/7

Find the area of a rhombus each side of which measurers 20 cm and one of whose diagonals is 24 cm.

RS Aggarwal - MathematicsThe diagonals of a rhombus are 48 cm and 20 cm long. Find the perimeter of the rhombus.

RS Aggarwal - MathematicsFind the area of a rhombus whose diagonal are 48 cm and 20 cm long.

RS Aggarwal - MathematicsIn a four sided field, the length of the longer diagonal is 128 m. The lengths of perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 17.3 m. Find the area of the field.

RS Aggarwal - MathematicsThe length of the diagonal of a square is 24 cm. Find its area.

RS Aggarwal - MathematicsOne side of a rectangle is 12 cm long and its diagonal measures 37 cm. Find the other side and the area of the rectangle.

RS Aggarwal - MathematicsA room 4.9 m long and 3.5 m broad is covered with carpet, leaving an uncovered margin of 25 cm all around the room. If the breadth of the carpet is 80 cm, finds its cost at RS. 80 per metre.

RS Aggarwal - Mathematics