# Grade 8 Perimeter and Area Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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Where,

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## (18) Find the Area of Shaded Region. (Take Π = 22/7 or Π = 3.14)

(a)

Each circle/semi circle having same diameter 7 cm. PQRS is a square.

(a)

## (20) Find Area of Shaded Region. (Take Π = 22/7 or Π = 3.14)

(a)

• Given figure is a trapezium quadrilateral.
• And formula for area of trapezium is as below,

• Here

• So, Area of given figure is

• As shown below, given figure is made of two equal parallelograms.
• Formula for area of Parallelogram is as below.

• Where ,

• Now, given figure is made of 2 equal parallelograms.
• Hence Area of given figure,

• Area of given figure

• Given figure is a parallelogram quadrilateral.
• Figure can be representing as below.
• Formula for Area of Parallelogram is as below

• Where ,

• Hence area of given parallelogram

• As shown below, given figure is made two equal trapeziums.
• Formula for area of trapezium is as below,

• Where,

• Given figure is made of two trapezium,
• Area of given figure

• Hence Area of given figure

• Given figure is Kite Quadrilateral.
• Formula for Area of Kite is as below.

• Where,

• Area of given figure

• As shown below, for the area of rhombus ABCD,

• Where,

• Now as show in figure is a right angle triangle,

• Diagonal AC

• Now, Diagonal BD

• Now,
• Where,

• Area of Given Shape

• Given Figure is made of 4 Triangle.
• So, area of Polygon is summation of area of this 4 triangle.
• Area of Polygon PQRST

• Area of :

• Area of :

• Area of :

• Area of

• Now, Area of Polygon PQRST

• Therefore, area of Polygon PQRST is

• Given Quadrilateral is made of two Triangle as shown in Figure

• Now, Area of ,

• Now, Area of ,

• Now, Area of quadrilateral STAR

• Therefore, area of quadrilateral STAR is

• Given Quadrilateral is made of two Triangle as shown in Figure

• Now, Area of

• Now, Area of :

• For FS;

• Now,

• Now, Area of quadrilateral FAST

• Therefore, area of quadrilateral FAST is

• Given Polygon is made of 4 triangles and one trapezium.
• Area of polygon is summation of all this 4 triangle and one trapezium

• Area of :

• Area of :

• Now,

• Area of :

• Now,

• Area of :

• Area of trapezium NORM:

• Where,

• Now,

• Where d is Diameter of Circle.

• Now,
• Where d is Diameter of circle = 35 cm (derived above)

• The ratio of circumference of two circle are hence,

• Where

• Now,
• Ratio of Area of this two Circle,

• Hence ratio of the areas of this two circles is

• A bike՚s tyre makes 1500 rotations to cover 2.355 km
• So,

• So, we can say that 1.57m is a circumference of bike՚s tyre

• Where

• So, Diameter of Bike՚s tyre is

• The circular track has radius
• So, Diameter of Circular Track (d)
• Diameter of Circular Track

• Now, Vikas complete 14 rounds of Track , so he travel total distance

• So, Vikas total travel 26.400 km distance in 3 hours
• Average speed of Vikas

• Suppose initially the radius of circle is
• And when Circle՚s area increase by four times its radius become
• Hence,

• When Circle Area Increase Four times than,

• Hence, The radius of a circle was Doubled, due to which the circle՚s area increase by four times

• A Car is moving at a speed of 88 km/h.
• Means car is travelling m/h.
• Now Diameter of car՚s wheel (d) is 140 cm
• Now ,

• That means if car travel 4.4 meter than its wheel complete one rotation.

• So, cars wheel rotating 20,000 times per hour

• There are two figures in give figure.

• Now, as shown in figure given triangle is right angle triangle and its hypotenuse is a diameter of circle (d) .
• So, for right angle triangle,

• Hence Diameter of Given circle is 13 cm
• Now, area of triangle:

• Now, area of circle:

• Now, area of shaded part

• As shown in figure Side of Square
• So,

• Now,
• Where d is diameter of circle = 7 cm

• Now as shown in below figure there are 3 full circle inside the square.

• Area of Circle:
• Circle having 14 cm diameter (d) .

• Area of Rectangle:
• Long side of rectangle (b)
• Small Side of Rectangle (a)

• Now, area of shaded part

• Now, Area of Rectangle:
• Long side of rectangle (b)
• Small Side of Rectangle (a)

• Area of Circle:
• Circle having 14 cm diameter (d) .

• Area of Trapezium:
• Long side of Trapezium (a)
• Small Side of Trapezium (b)
• Height of Trapezium

• Now As shown in figure there are one circle , and 2 trapezium in the figure,
• So, area of shaded Part

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