Areas of Different Plane Figures

Q.

On increasing the length of a rectangle by 20% and decreasing its breadth by 20%, what is the change in its area ?

(a) 20% increase (b) 20% decrease (c) No change (d) 4% decrease

Q.

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 $m^2$. Find the width of the path.

Q.

The perimeter of a rectangular field is 82m and its area is $400m^2.$ Find the breadth of the rectangle.

Q.

In the centre of a rectangular lawn of dimensions $50m\times 40m,$ a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184m^2.$ Find the length and breadth of the pond.

Q.

Is it possible to design a rectangular park of perimeter 80m and area $400m^2$? If so, find its length and breadth.

Q.

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, $\angle$ ACB = ${90}^o$ and AC = 15 cm.

Q. Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

Q.

One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is

(a) 192 $c{m}^2$ (b) 480 $c{m}^2$ (c) 240 $c{m}^2$ (d) 384 $c{m}^2$

Q.

A square of side 4cm is inscribed in a circle. Find the area enclosed between the circle and square.

Q.

Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is $800m^2$? If so, find its length and breadth.

Q. Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square .

Q.

A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.

Q.

The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per $m^2$. Find the cost of ploughing the field in Rupees. (Take $\pi =\frac{22}{7}$). [3 MARKS]

Q.

Question 87

A floor is 4.5 m long and 3.6 m wide A 6 cm square tile costs Rs. 23.25.
What will be the cost to cover the floor with these tiles?

Q.

The diagonals of a rhombus are 8 cm and 15 cm. Find its side.

Q. If the radius of a circle is increased by 40%.What will be its increase in area?

Q. The length of a chain used as the boundary of a semicircular park is 108 m. Find the area of the park.

Q.

Question 72

In 2007-08, the number of students appeared for Class X examination was 105332 and in 2008-09 the number was 116054. If 88151 students pass the examination in 2007-08 and 103804 students in 2008-09. What is the increase or decrease in pass percentage in class X result?

Q. Question 11
Find the area of the shaded region in figure, where arcs drawn with centres, A, B , C and D intersect in pairs at mid - point P, Q, R and S of the sides AB , BC , CD and DA, respectively of a square ABCD (use $\pi =3.14$)

Q.

A carpet of size $5m\times 2m$ has $25cm$ wide red border. The inner part of the carpet is blue in colour. Find the area of blue portion. What is the ratio of areas of red portion to blue portion?

Q.

The perimeter of a rhombus is $60cm.$ If one of its diagonals is $18cm$ long, find (i) the length of the other diagonal, and (ii) the area of the rhombus.

Q.

A farmer has 70m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600sq.m , find the length of its shorter side.

Q.

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.

Q.

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203cm². Determine the sides of the two squares.

Q.

ABCD is a square of side 10 cm. The area of the shaded region will be

1. 60 cm²

2. 75 cm²

3. 57 cm²

4. 80 cm^2‑

Q. The area of a sector whose perimeter is four times its radius r units, is

(a) $\frac{r^2}{4}$ sq. units

(b) 2r² sq. units

(c) r² sq.units

(d) $\frac{r^2}{2}$sq. units

Q.

The area of a square field is $0.5$ hectare. The length of its diagonal is

(a) $150m$ (b) $100\sqrt{2}m$ (b) $100m$ (b) $50\sqrt{2}m$

Q.

Question 11

Find the area of the quadrilateral ABCD.
Here, AC = 22 cm, BM = 3 cm, DN = 3 cm and BM $\perp$ AC, DN $\perp$ AC.

Q.

Find the area of a trapezium whose parallel sides are $11cm$ and $25cm$ long, and the nonparallel sides are $15cm$ and $13cm$ long.

Q.

On a square handkerchief, nine circular designs each of radius 7 cm are made (see the given figure). Find the area of the remaining portion of the handkerchief.