Area of a Polygon

Q. If ABCDEF is a regular hexagon with each side equal to 6 cm and the distance of the circumcentre from any of the sides is 4 cm, then it's area is .

1. $64c{m}^2$
2. $72c{m}^2$
3. $59c{m}^2$

Q.

If the perimeter of a regular hexagon is 120 cm, Find its area.

1. BDEF is a parallelogram

2. Area of (DEF) = 1/ 4 Area of (ABC)

3. Area of (BDEF) = 1 /2 Area of (ABC)

4. All of these

Q.

If the perimeter of a regular hexagon is 60 cm, Find its area.

1. $100\sqrt{3}c{m}^2$

2. $150\sqrt{3}c{m}^2$

3. $120\sqrt{3}c{m}^2$

4. $160\sqrt{3}c{m}^2$

Q. In parallelogram ABCD, AB is 30 cm and area of the parallelogram is 120 sq. cm. What is the height of the parallelogram?

1. 4 cm
2. 5 cm
3. 3 cm
4. 2 cm

Q.

There is a regular octagonal park. The surface area of the park is ___ (in $m^2$ )

1. 119

2. 120

3. 200

4. 100

Q. In parallelogram ABCD, AB = 10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD.

Q.

Find the area of the parallelogram ABCD.

Given, BC = 5 cm and the corresponding altitude AP = 8 cm.

1. 20 cm²

2. 10 cm²

3. 30 cm²

4. 40 cm²

Q. Question 6
Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that $ar\left(APB\right)\times ar\left(CPD\right)=ar\left(APD\right)\times ar\left(BPC\right)$

Q.

Find the area of a regular hexagon with side length is 4 cm.

1. 52. 54

2. 41.56
3. 46.62
4. 56.62

Q.

ABCD is a parallelogram with sides AB and BC equal to 15 cm and 6 cm, respectively. If DF = 4 cm, what is the value of BE?

Q. Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm.

Q.

There is a regular octagonal park. The surface area of the park $=$___ $m^2$

Q.

The area of parallelogram ABCD is:

1. AB×BM
2. BC×BN
3. DC×DL
4. AD×BM

Q.

Area of Hexagon PQRSTU = Area of ∆PQN + Area of quad QRLN + Area of ∆RSL + Area of ∆TMS + Area of quad OMTU + Area of ∆POU

1. True

2. False

Q.

Hero's formula cannot be used in finding the area of quadrilateral.

1. True

2. False

Q. A regular hexagon is inscribed in a circle of radius $6$ cm. Find its area (in cm${}^2$).

1. $48\sqrt{3}$
2. $54\sqrt{3}$
3. $48\sqrt{2}$
4. $54\sqrt{2}$

Q. In the given figure, calculate the area of quadrilateral ABCD.

Q.

In the given figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Q. Match the figures with their areas.

1. $2c{m}^2$
2. $10c{m}^2$
3. $24c{m}^2$

Q.

If parallelogram ABCD and rectangle ABEM are of equal area, then:

1. Perimeter of AMEB = Perimeter of ADCB

2. Perimeter of AMEB $<$ Perimeter of ADCB

3. Perimeter of AMEB $>$Perimeter of ADCB

4. Perimeter of AMEB = $\frac{1}{2}$ Perimeter of ADCB

Q. In a quadrilateral ABCD, it is given that BD = 16 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 7 cm, then ar(quad. ABCD) = ?
(a) 256 cm²
(b) 128 cm²
(c) 64 cm²
(d) 96 cm²

Q. In the adjoining figure, ABCD is a quadrilateral in which diag. BD = 14 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8 cm and CM = 6 cm, find the area of quad. ABCD.

Q. The area of quadrilateral ABCD in the given figure is
(a) 57 cm²
(b) 108 cm²
(c) 114 cm²
(d) 195 cm²

Q. Area (hexagon PQRSTU) = Area(triangle PQN) + Area(quadrilateral QRLN) + Area(triangle RSL) + Area(triangle SMT) + Area(quadrilateral MTUO)

1. False
2. True