Area of Plane Figures

Q.

Question 97

Find the area enclosed by the following figure:

Q.

(i) ABCD is a trapezium in which AB || DC. Diagonals AC and BD intersect each other at O. Find the triangle which is equal to the area of $△$ BOC.

(ii) If AB = 6 cm, DC = 10 cm and perpendicular distance between AB and DC is 8 cm, then find the area of $\square$ ABCD.

Q.

In the given figure an equilateral triangle has been cut into two equal parts.

What is the area of the 1st part ?

1. $\frac{\sqrt{3}}{2}$ sq. units

2. $\sqrt{3}$ sq. units

3. 2$\sqrt{3}$ sq. units

4. 3 sq. units

Q.

Find the area of the shaded region in figure.

Q.

What is the area of the triangle ACD?

1. $4c{m}^2$

2. $2\sqrt{2}c{m}^2$

3. $8\sqrt{2}c{m}^2$

4. $4\sqrt{2}c{m}^2$

Q.

In the given figure, what is the area of the triangle ACD?

1. $2m^2$

2. $\sqrt{2}{m}^2$

3. $1m^2$

4. $2\sqrt{2}{m}^2$

Q. If $y=\sqrt{\sqrt{7}+7+\sqrt{8+2\sqrt{7}}}-\sqrt{7}$, then find the value of $y$. [3 marks]

Q.

What is the area of the right triangle with lengths of perpendicular sides equal to 2 cm each?

1. 4 $c{m}^2$

2. $\sqrt{2}c{m}^2$

3. 2 $c{m}^2$

4. 2$\sqrt{2}c{m}^2$

Q.

ADC is a right angled isosceles $△$ with right angle at D. What should be the area of $△$ AFE?

1. $2squnits$

2. $2\sqrt{2}squnits$

3. $1squnits$

4. $\sqrt{2}squnits$

Q.

Find the side of the square if area is $7.29m^2.$

Q. The area of the region bounded by $y=|x-1|$ and $y=1$ in sq. units is

1. $1$
2. $3$
3. $1$ $/2$
4. $4$

Q.

What is the area of the $△$ SOR? PQRS is a square.

1. $2c{m}^2$

2. $2\sqrt{2}c{m}^2$

3. $\frac{1}{2}c{m}^2$

4. $1c{m}^2$

Q.

The area of a square can be represented by the expression $x^{10}$ .

What represents a side of the square?

Q.

If AB = 2 m, Find the Area of the $△$ EOA. E is the midpoint of AB.

1. $\frac{1}{4}{m}^2$

2. $\frac{1}{2}{m}^2$

3. $1m^2$

4. $\frac{3}{4}{m}^2$

Q.

If $\sqrt{0.5}$ and $\sqrt{8}$ are the length and width of a rectangle, then find the area of the rectangle.

1. 2.8 square units

2. 2 square units

3. 3 square units

4. 1.8 square units

Q.

The triangle BDC is right angled. If BD measures $2\sqrt{2}$ cm, what is the area of the square?

1. 2 $c{m}^2$

2. $2\sqrt{2}c{m}^2$

3. 4 $c{m}^2$

4. $\sqrt{2}c{m}^2$

Q.

What is the Area of the triangle ACD?

1. $3\sqrt{2}{m}^2$

2. $2m^2$

3. $2\sqrt{3}{m}^2$

4. $2\sqrt{2}{m}^2$

Q.

Find the Area of the Square ADEC given in the figure.

1. 2$\sqrt{2}$ square units

2. $\sqrt{2}$ square units

3. 2 square units

4. 4 square units

Q.

If $\sqrt{5}$ and $\sqrt{2}$ are the length and width of a rectangle, then find the area of the rectangle.

1. 2.1622 square units

2. 3.1652 square units

3. 3.1622 square units

4. 4.1622 square units

Q. The given figure shows a pentagon $ABCDE$ .$EG$ drawn parallel to $DA$ meets $BA$ producedat G and $CF$ drawn parallel to $DB$ meets $AB$ produced at $F$ .
Prove that the area of pentagon $ABCDE$ is equal to the area of triangle $GDF$ .

Q.

Find the area of the $△$AEF if EF = 1 m.

1. $2m^2$

2. $4m^2$

3. $1m^2$

4. $\sqrt{2}{m}^2$

Q.

Find the area of the square if its perimeter is $36cm$