Areas of Different Plane Figures

Q.

Two parallel sides of a trapezium are 60cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.

Q.

The area of trapezium ABCD in the given figure is

(a) $62c{m}^2$

(b) $93c{m}^2$

(c) $124c{m}^2$

(d) $155c{m}^2$

Q. Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

Q.

Compute the area of trapezium PQRS in the figure.

Q. Question 2
In figure, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region.

Q.

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then $ar\left(△RAS\right)$ is

Q.

In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle of radius 10 cm.If AD=2$\sqrt{5}$ cm then area of the rectangle is

(a) $32c{m}^2$

(b) $40c{m}^2$

(c) $44c{m}^2$

(d) $48c{m}^2$

Q.

A rectangular lawn, 75 m by 60 m, has two roads, each road 4 m wide, running through the middle of the lawsn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at Rs 50 per $m^2.$

Q.

The figure formed by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a

(a) rectangle of area $24c{m}^2$

(b) square of area $24c{m}^2$

(c) trapezium of area $24c{m}^2$

(d) rhombus of area $24c{m}^2$

Q.

ABCD is a tapezium with parallel sides AB = a and DC = b. If E and F are mid points of non parallel sides AD and BC respectively, then the ratio of areas of quadrialaterals ABFE and EFCD is

1. (3a + b) : (a + 3b)
   

2. (a + 3b) : (3a+b)

3. (2a+ b ) : (3a + b)
   

4. a : b
   

Q.

Given expression is the formula for area of Trapizium:
$\frac{1}{2}$ {(sum of parallel sides) × h}

1. Area of rhombus

2. Area of rectangle

Q.

In the figure, OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If $DE=2\sqrt{5}$ then find the area of the rectangle.

Q.

In trapezium $ABCD,AB=16cm,CE=4cm$ and the area of trapezium $=50c{m}^2$. Find $CD$.

1. $5cm$

2. $9cm$

3. $10cm$

4. $12cm$

Q.

The area of figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm is

1. A rhombus of area $24c{m}^2$
   

2. a rectangle of area $24c{m}^2$
   

3. a trapezium of area $14c{m}^2$
   

4. a square of area 26 cm^2

Q.

Question 2
Find the area of a quadrilateral ABCD in which AB=3cm, BC=4cm, CD=4cm, DA = 5cm and AC= 5cm.

Q. 14. In one side of a rhombus is "a" and one diagonal is "d1" then its area will be

Q. Question 3
The area of a trapezium is 475 $c{m}^2$ and the height is 19cm. Find the lengths of its two parallel sides, of one side is 4cm greater than the other.

Q.

1. $110$ sq. cm
2. $120$ sq.cm
3. $125$ sq. cm
4. $130$ sq. cm

Q.

area of rhombus

Q. Area of a rhombus is equal to one-half of the product of the lengths of___

Q.

The area of trapezium $=\frac{1}{2}\times$ length of the base $\times$ distance between two parallel lines

1. True

2. False

Q. when we apply the area ofo rhombus as base ? height?

Q. The average weight of $39$ students in a class is $23$kgs. Among them Sita is the heaviest while Tina is the lightest. If both of them are excluded from the class still the average remains same. The ratio of weight of Sita to Tina is $15:8$, then what is the weight of the Tina?

Q. If the area of circle is equals to its perimeter what will be measure of its radius?​

Q. the area of a rhombus is 72 cm square. if one of the diagonals is 18 cm, find the length of the other diagonal

Q. The ost of cultivating a square field at the rate of Rs. 160 per hectare is Rs 1440. Find the cost of putting a fence around it at the rate of 75 paise per meter.

Q. The ratio of the length of a vertical pole and its shadow on the ground is $5:3$. Find the length (in meter) of the shadow if the length of the pole is $80$ meters.

Q. The shape of the cross-section of a canal is a trapezium if the canal is $10$ m wide at the top, $6$ m wide at the bottom and the area of its cross-section is $72{\text{m}}^2,$ find the depth of the canal.