Area Based Approach

Q.

The area of the triangle with vertices $P\left(z\right)$, $Q\left(iz\right)$ and $R(z+iz)$ is:

1. $\left(\frac{1}{2}\right){\left|z+iz\right|}^2$

2. $1$

3. $\frac{1}{2}$

4. $\left(\frac{1}{2}\right){\left|z\right|}^2$

Q. In the adjoining figure ABCD, P and R are the mid-points of the sides AB and CD. ABCD is a parallelogram. What is the ratio of the shaded to the unshaded region?

1. $Noneofthese$
2. $\frac{1}{2}$
3. $\frac{1}{3}$
4. $\frac{1}{4}$

Q.

What is the ratio of shaded area to the area of hexagon?

1. 
   

2. 
   

3. 
   

4. 
   

Q.

A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is:

1. 10 m × 10 m

2. None of these

3. 20 m × 5 m

4. 30 m × 3.33 m

5. 40 m × 2.5 m

Q.
As shown in the figure, triangle PAB is formed by the three tangents to the circle with center O and $\angle APB={40}^{\circ }.\angle AOB$ equals:___

Q.

The figure below is a regular octagon. What fraction of its area is shaded?

1. 1/3

2. 3/8

3. 1/5

4. 1/4

Q.

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides 37 feet, then what is the area of the parking space in square feet?

1. 81 sq. ft

2. 46 sq. ft

3. 252 sq. ft.

4. 126 sq. ft.

5. 265 sq. ft

Q.

What is the area of a parallelogram and triangle?

Q. $\Delta$ABC is an equilateral triangle of side 14 cm. A semi circle on BC as diameter is drawn to meet AB at D, and AC at E. Find the area of the shaded region?

1. 
2. 
3. 49 cm²
4. 49sqrt(2) cm²

Q. The area of regular hexagon ABCDEF is 144. Then, the area of shaded region is ___.

Q.

If $A$ and $B$ are two points on the line $3x+4y+15=0$ such that $OA=OB=9$ units, then the area of the triangle $OAB$ is

1. $18$ sq. units

2. $18\sqrt{2}$ sq. units

3. $\frac{18}{\sqrt{2}}$ sq. units

4. None of these

Q. The inside perimeter of a running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.

1. $1273.14m^2$
2. $5166m^2$
3. $5802.57m^2$
4. $636.32m^2$

Q.

On a square cardboard sheet of area $784c{m}^2$, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

Q. In the adjoining figure there are two congruent regular hexagons each with side 6 cm.


What is the ratio of area of $\Delta BDF$ and $\Delta PQR$, if P, Q and R are the mid-points of side AF, BC and DE?

1. 6 : 5
2. 7 : 6
3. 1 : 1
4. 4 : 3

Q.

A rectangle is drawn so that none of its sides has a length greater than 'x'. all lengths lesser than 'x' are equally likely. The chance that the rectangle has its diagonal greater than 'x' is (in %)?

1. 21.5%

2. 66.66%

3. 33.33%

4. 29.3%

Q.

The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points ?

1. Equilateral triangle of side 5√3cm

2. Isosceles triangle in which the equal sides measure 5√2cm

3. Isosceles triangle in which the unequal side measures 5√2cm

4. Equilateral triangle of side 5cm

Q. Four goats are tethered at four corners of a square plot of side 2 metres (m) so that the adjacent goats can just reach one another. There is a small circular pond of area 0.5 m² at the centre. Find the ungrazed area.

1. 0.5m²

2. 0.2m²

3. 0.36m²

4. 1m²

Q. A rectangular plate is of 6m breadth and 12 m length. Two apertures of 2 m diameter each and one aperture of 1 m diameter have been made with the help of a gas cutter. What is the area of the remaining portion of the plate?

1. None of these
2. 68.5 sq.m
3. 62.5 sq.m
4. 65 sq.m

Q.

In the figure shown below, all the vertical lines are parallel to each other & are equally spaced. All the horizontal lines are parallel to each other and are equally spaced. What fraction of the area of ABCD, is shaded?

1. 
   

2. 
   

3. 
   

4. 
   

Q.

A square is inscribed inside a square ABCD such that the vertices of the smaller square lies on the midpoints of the sides of the square ABCD. Find the ratio of the area of the square ABCD to that of the smaller one.

1. 5

2. 8

3. 3

4. 4

5. 2

Q. ABCDEF is a regular hexagon. PR= $\frac{1}{3}$ AF, QS= $\frac{1}{3}$ BC and PQ is parallel to RS. Also TE= $\frac{1}{3}$ FE and UD= $\frac{1}{3}$ CD and TU is parallel to ED. Find the ratio of shaded regions to the hexagon ABCDEF.

1. 1:3
2. 1:4
3. 8:27
4. 17:54

Q.

The length of a minute hand of a wall clock is 10.5 cm. The area swept by it in 10 minutes would be -

1. 51.75 cm²

2. 5.77 cm²

3. 59.25 cm²

4. 57.75 cm²

5. 51.25 cm²

Q.

The cost of fencing of field C is what percent of the cost of fencing of field D?

1. 87.54%

2. 67.5%

3. 46.5%

4. 72.13%

5. 54.36%

Q.

ABCD is a square and E is the midpoint of CD. Find the ratio of unshaded point to that of shaded region.

1. 3:1

2. 2:1

3. 1:3

4. 1:2

5. 1:4

Q. In the figure below, C is the center of the square. Find the area of the shaded area?___

Q.

An athletic track is designed in such a way that an athlete runs the 1${}^{st}$ and 3${}^{rd}$ quarters of the race around a circular track and the 2${}^{nd}$ and 4${}^{th}$ quarters around a square track. (As shown in the figure below) If the area of the entire square field is 256 sq units, what is the area enclosed by the running track? (Assume that the track touches the boundary of the field at the midpoints of the four sides and the width of the track is negligible).

1. 64 + 32π sq units

2. 32 + 32π sq units

3. 32 + 16π sq units

4. 64 + 16π sq units

Q. In the adjoining figure O is the centre of the circle with radius 'r' AB, CD and EF are the diameters of the circle. $\angle OAF=\angle OCB={60}^{\circ }$. What is the area of the shaded region?

1. $\frac{r^2}{2}(\pi -\frac{3\sqrt{3}}{2})$
2. $\frac{r^2}{2}(\pi -\frac{3\sqrt{3}}{4})$
3. $Datainsufficient$
4. $\frac{r^2}{3}(\pi -\frac{2\sqrt{3}}{3})$

Q. ΔABC is an equilateral triangle of side 14 cm. A semi circle on BC as diameter is drawn to meet AB at D, and AC at E. Find the area of the shaded region.

1. 
2. 49sqrt(2) cm²
3. 
4. 49 cm²

Q.

PQR is a right angled triangle with PQ=8, QR=6, QT as altitude. If a circle is drawn with QT as diameter, what is the area of the shaded region?

1. 
   

2. 
   

3. 
   

4. 
   

Q.

In the figure given below, E is the mid-point of AB and F is the midpoint of AD. If the area of FAEC is 13, what is the area of ABCD?

1. 19.5

2. 26

3. 39

4. None of these