Perimeter And A...

The figure shows the length and breadth of a rectangle in inches.



How much is the shaded area in square inches?

What is the area of the shaded portion in the given figure?

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.



What is the proportion of the sheet area left after punching?

One side of a rhombus is 10 cm and one of its diagonals is 12 cm. The area of the rhombus is

In the diagram, ABC is equilateral, BC = 2CD, AF = 6, and DEF is perpendicular to AB. What is the area of quadrilateral FBCE?

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.



Find the area of the part of the circle (round punch) falling outside the square sheet.

Based on the figure shown below, what is the value of x, if y = 10?

In the figure given below, AC + AB = 5 AD and AC – AD = 8 units. What is the area of the rectangle ABCD?

In a circle of radius 49 cm, an arc subtends an angle of 72^o at the centre. Find the length of the arc and the area of the sector.

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.
BAC = 30° and AB = AC = 10 m.



What is the area that can be grazed by the cow, if the length of the rope is 8 m?

The lengths of sides of a triangle are 5 units, 12 units and 13 units. A rectangle is constructed which is equal in area to the triangle. The rectangle has a length of 10 units. What is the perimeter of the rectangle?

The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at point B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?

A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 m², how wide (in metres) is the walkway?

PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR = OS. What is the ratio of the area of the circle to the area of the square?

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.
BAC = 30° and AB = AC = 10 m.



What is the area that can be grazed by the cow, if the length of the rope is 12 m?

Four identical coins are placed in a square. For each coin, the ratio of area to circumference is same as the ratio of circumference to area. Find the area of the square that is not covered by the coins.

Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after three of them have travelled the distances of 40 m, 50 m and 60 m. The maximum distance that the fourth could have travelled is approximately

AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of quadrilateral ACBD.

The sum of the areas of two circles, which touch each other externally, is 153m². If the sum of their radii is 15 m, find the ratio of the larger to the smaller radius.

Three identical cones with base radius r are placed on their bases such that each is touching the other two. What is the radius of the circle drawn through their vertices?