# Area of a Quadrilateral

## Trending Questions

**Q.**

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

**Q.**

Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD=900 and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3=1.73)

**Q.**

Let ${A}_{1},{A}_{2},{A}_{3},\dots .$be squares such that for each $n\ge 1$, the length of the side of ${A}_{n}$ equals the length of diagonal of ${A}_{n+1}$. If the length of ${A}_{1}$ is $12cm$, then the smallest value of $n$ for which area of ${A}_{n}$ is less than one is ____________.

**Q.**

Find the area of a quadrilateral ABCD in which AB = 42cm, BC = 21cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.

**Q.**

The sides of a quadrilateral taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.

**Q.**

While reading a newspaper, Ted caught news of a football match between Brazil and Spain. The countries were represented with their respective flags. In Brazil’s flag, the length of any side of the parallelogram is 10.6 cm and the corresponding height is equal to 8.3 cm. If the area of the green region is 74.02 cm2 and length of the flag is twice the breadth, find the length of the flag.

9 cm

18 cm

19 cm

9.5 cm

**Q.**

A field is in the shape of a trapezium whose parallel sides are 25m and 10m. If its non-parallel sides are 14m and 13m. Its area =

**Q.**

The area of the square inscribed in a semicircle is 2 cm2. If the semi-circle is extended to a full circle, the area of the square inscribed in this circle is

6 cm2

7 cm2

4 cm2

5 cm2

**Q.**

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm AD = 9cm, CD = 12cm, ∠ACB=900and AC = 15cm.

**Q.**

A triangle and parallelogram are constructed on the same base such that their area are equal. If the altitudes of the parallelogram is$100m$, then find the altitude of the triangle.

**Q.**

The dimensions of a rectangular field are $80\mathrm{m}$ and $18\mathrm{m}$. Find the length of its diagonal.

**Q.**In the given figure, PQRS is a parallelogram and PQ = 8 cm. If area of triangle PXQ is 32 sq cm, find the altitude of the parallelogram.

- 10 cm
- 4 cm
- 8 cm
- 12 cm

**Q.**

The area of quadrilateral ABCD is:

128 cm

^{2}114 cm

^{2}76 cm

^{2}57 cm

^{2}

**Q.**

In the given figure OABC is a rhombus, three of whose vertices lie on a circle with center O.

If the area of the rhombus is 50√3 cm2,

then the area of the circle is sq cm. (Take π=3.14)

31.4

300

314

341

**Q.**

If the area of a rhombus-shaped box is 6√7cm2 and its one diagonal is 6cm. Find the side of the rhombus.

4cm

5cm

8cm

3cm

**Q.**

Draw triangle of sides 6, 7 and 8 centimetres. Divide it into three triangles whose areas are in the ratio 1 : 2 : 3.

**Q.**

The area of a regular hexagon of side ‘a’ is the sum of the areas of the ___ equilateral triangles with side a.

6

4

8

5

**Q.**

What is the area of regular octagon inscribed in a circle of radius r units.

**Q.**

Find the area of a parallelogram ABCD in which AB = 3 cm and BC = 4 cm and AC = 5 cm using Heron's formula.

18 cm

^{2}12 cm

^{2}24 cm

^{2}6 cm

^{2}

**Q.**

A water tank in the shape of a prism has isosceles trapeziums as bases whose dimensions are shown below.

The length of the tank is 80 centimetres. How many litres of water can it contain?

**Q.**

ABCD is a parallelogram and 'Q' is a point on AB. If area of QCD is 10 sq cm, then find the ar(QAD) + ar(QBC) in sq cms.

- 10

**Q.**

The parallel sides of an isosceles trapezium are in the ratio 2:3. If its height is 8cm and area is 240cm2, then its perimeter is

96

100

80

60

**Q.**

In the given figure, ABCD is a parallelogram and PD is parallel to QC.

S1 : △APD ≅ △BQC

S2 : ar(△APD) + ar(PBCD) = ar(△BQC) + ar(CDPB)

S1 is true but S2 is false

S1 is false but S2 is true

S1 and S2 are both true and S2 is the explanation for S1

S1 and S2 are are both true and S1 is the explanation for S2

**Q.**

The diagonals of a quadrilateral PQRS, PR and SQ intersect at O. If QO = OS, then find the area of triangle PQR given PR = 10 cm and altitude ST = 5 cm.

- 30 cm2
- 10 cm2
- 15 cm2
- 25 cm2

**Q.**

If the side of a rhombus is 6 cm and its one diagonal is 8 cm. Find the area of the rhombus in cm2.

3√9

16√5

8√5

9√3

**Q.**

A cone 12cm high is cut 8cm from the vertex to form a frustum with a volume of 190cu.cm. Find the radius of the cone.

**Q.**

Find the area of the parallelogram ABCD.

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

- 20 cm2
- 10 cm2
- 40 cm2
- 30 cm2

**Q.**Write True or False justify your answer :

If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of rhombus is 96 cm2

**Q.**Construct a Δ ABC, in which base BC = 3 cm, ∠B = 30° and AB + AC = 5.2 cm.

**Q.**

In quadrilateral ABCD the diagonals intersect at O and AB ∥ CD . The areas of triangles AOB and DOC are equal and altitude of △AOB = 5 cm. The area of triangle ABC is _______

75 cm

^{2}45 cm

^{2}105 cm

^{2}90 cm

^{2}