Area of Square, Rectangle, Parallelogram, Rhombus, and Trapezeum-RRB

Square:

A square is a four sided figure created by connecting four line segments. All of the line segments are of the same length and they come together to form four right angles. All four sides are equal and four angles are equal = 90 degree.

If a is each side of a square then Perimeter = 4 a, and area of a square A = a

The diagonals of a square are equal and bisect each other at right angles.

 

 

Area Of Rectangle

 

 

 

A rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal.
If two opposite sides of a rectangle are w and h then perimeter.

Perimeter of a rectangle = 2(Length + Breadth) = 2(w + h)

Area of a rectangle = (Length x Breadth).
Area = w x h

Diagonals of a rectangle are equal and bisect each other

Rhombus :

A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) meet in the middle at a right angle. In other words they “bisect” (cut in half) each other at right angles.A rhombus is a special type of parallelogram of four equal sides. The diagonals of a rhombus are unequal and bisect each other at right angles.

 

 

 

The area is the product of two adjacent sides. i.e ba. b is the length of the base a is the altitude (height).

Another simple formula for the area of a rhombus when we know the lengths of the diagonals.
The area is half the product of the diagonals. As a formula:

Area  = \( \frac{1}{2}\)(d1 x d2)

Where d1 is the length of a diagonal. d2 is the length of the other diagonal

Parallelogram :

A parallelogram is a four-sided plane rectilinear figure with opposite sides parallel.
A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
Area of parallelogram = (Base x Height).

 

 

 

 

Trapezium :

 

 

 

A trapezium is a quadrilateral with one pair of sides parallel.
Area of a trapezium = \(\frac {b}{2}\)x (sum of parallel sides) x distance between them.

Area = \(\frac {b}{2}\)h (a +b )

Question – 1

The respective ratio of the length and breadth of rectangular plot is 3:2. If the length of the plot is 40 meters more than its breadth, what is the perimeter of the rectangular plot?

(1) 300 meters

(2) 400 meters

(3) 500 meters

(4) Can not be determined

(5) None of these

Answer : (2) 400 meters

Question – 2

The area of a square is three-fifth the area of a rectangular. The length of the rectangular is 25 cms. and its breadth is 10 cms less than its length. What is the perimeter of the square ?

(1) 80 cms

(2) 44 cms

(3) 60 cms

(4) 48 cms

(5) None of these

Answer : (3) 60 cms

Question – 3

The length of a rectangular is 16 cms. which is 2 cms. more than the diameter of a circle. What is the area of the circle?

(1) 112 Sq. cms.

(2) 161 Sq. cms.

(3) 160 Sq. cms.

(4) 132 Sq. cms

(5) 154 Sq. cms

Answer : (3) 154 cms

Question – 4

The area of a circular plot is twice the area of a rectangular plot. If the area of the rectangular plot is 11088 sq. meters. What is the perimeter of the circular plot?

(1) 572 meters

(2) 528 meters

(3) 440 meters

(4) 484 meters

(5) 576 meters

Answer :(2) 528 meters

Question – 5

The area of a rectangle is four-third the area of a square. The area of the square is 729 sq. cms and the length of the rectangle is 81 cms. What is the difference between the side of the square and the breadth of the rectangle ?

(1) 15 cms.

(2) 18 cms.

(3) 27 cms.

(4) 24 cms.

(5) None of these

Answer : (1) 15 cms

Question – 6

The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cms. and 43 cms. respectively. What is half the radius of the circle ?

(1) 28 cms.

(2) 27 cms.

(3) 15 cms.

(4) 24 cms.

(5) None of these

Answer :(3) 15 cms

Question – 7

The area of a rectangle is 1.8 times the area of a square. The length of the rectangle is five times the breadth. The side of the square is 20 cm. What is the perimeter of the rectangle ?

(1) 145 cm

(2) 132 cm

(3) 145 cm

(4) 144 cm

(5) None of these

Answer: (4) 144 c

Question – 8

The side of a square is 5 cm. which is 13 cm, less than the diameter of a circle. What is the approximate area of the circle ?

(1) 225 sq. cm

(2) 265 sq. cm

(3) 255 sq. cm

(4) 275 sq. cm

(5) 245 sq. cm

Answer : (3) 255 sq. cm

Question – 9

The breadth of a rectangular field is 25 meters. The total cost of putting a grass bed on this field was Rs. 12,375 at the rate of Rs. 15 per meter². What is the length of the rectangular field?

(1) 37 meter

(2) 33 meter

(3) 32 meter

(4) 34 meter

(5) 30 meter

Answer : (2) 33 meter

Question – 10

The cost of putting a grass bed is Rs. 75 per sq. meter. The length of a rectangular field is 15 meter and the breadth is 4 meter less than the length. What will be the total cost of putting a grass bed on the field?

(1) Rs. 12,365

(2) Rs. 12,957

(3) Rs. 12,356

(4) Rs. 12,375

(5) None of these

Answer :(4) Rs.12,375