Mensuration Exercise 2

In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area.

ABCD is a parallelogram. P, Q, R and S are points on sides AB, BC, CD and DA, respectively such that AP = DR. If the area of the rectangle ABCD is 16 cm², then the area of the quadrilateral PQRS is:

The cross section of a canal is a trapezium in shape. If the canal is 7 metres wide at the top and 9 metres at the bottom and the area of cross-section is 1280 square metres, find the length of the canal.

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is:

Two sides of a plot measure 32 metres and 24 metres and the angle between them is a perfect right angle. The other two sides measure 25 metres each and the other three angles
What is the area of the plot?

One diagonal of a rhombus is 24cm side is 13 cm Find the area of the rhombus.

When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to

The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions? [use π = ²²⁄₇].

A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. ft. per day, then approximately what time will be taken by the cow to graze the whole field?

A wire is looped in the form of a circle of radius 28 cm. It is re-bent into a square form. Determine the length of a side of the square.

Semi-circular lawns are attached to both the edges of a rectangular field measuring 42 m × 35 m. The area of the total field is:

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle?

A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze?

How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 cm² for each plant?

From a square piece of a paper having each side equal to 10 cm, the largest possible circle is being cut out. The ratio of the area of the circle to the area of the original square is nearly:

If the area of a circle decreases by 36%, then the radius of a circle decreases by

A circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside. Find the area of path.

Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the area enclosed between the circumferences of the circles is:

In a special racing event, the person who enclosed the maximum area would be the winner and would get ₹100 every square metre of area covered by him/her. Jonnson, who successfully completed the race and was the eventual winner, enclosed the area shown in the figure below. What is the prize money won? (Note: The arc from C to D makes a complete semi-circle).
AB = 3 m, BC = 10 m, CD = BE = 2 m

The figure shows a rectangle ABCD with a semi-circle and a circle inscribed inside it as shown. What is the ratio of the area of the circle to that of the semi-circle?

In ∆ACD, AD = AC and ∠C = 2∠E,. The distance between parallel lines AB and CD is h.

Then
I. Area of parallelogram ABCD
II. Area of ∆ADE

Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is:

In the adjoining the figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of the triangle CBE to that of the triangle ADE

The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ABC

There are two concentric circular tracks of radii 100 m and 102 m, respectively. A runs on the inner track and goes once round on the inner track in 1 min 30 sec, while B runs on the outer track in 1 min 32 sec. Who runs faster?