*Area of rectangle (A) =length x breadth (I x b) *Perimeter (P) = 2 x (length breadth) = 2(lb)
EXAMPLES
1.
The breadth of a rectangular filed is 80% of its length. Find the area of the field if its perimeter is__ Let x metres be the length of the rectangular filed. Then, Breadth =80/100x=4/5x =4/5x Perimeter = 2(1 b) = 90 cm .'.90 = 2(x4x/5) 90 = 2(9x/5) 18x/5=90 x=90*5/18 .'.length = 25 cm Area = I x b = 25x80/100x25 = 500 cm2
2.
The perimeter of a rectangle is 48cm: If the length of the rectangle is 16 cm, find the ratio between length and breadth. 2(1 b) =48 ie, 2(16 b) = 48 32 2b = 48 2b = 16 .'.b = 8 .'. I :b= 16:8 = 2:1
3.
If the length and breadth of a rectangular plot be increased by 50% and 20% respectively, then how many times will its area be increased? Let x metres be the original length and y metres be the original breadth. Then, original area = (xy)m2 New length = (150x/100)m =(3/2x)m New breadth = (120 /100y)m=(6/5y)m New area=(3/2x*6/5y)m2 =9xy/5 m2 .'.Increase=4/5xy/xy=4/5 times
4.
A rectangular grassy plot is 112 metres by 78 metres. It has a gravel path 2.5 metres wide all around it inside. Find the area of the path and the cost of constructing it at 80 paise per 1000cm2. Area of the path = Area of grassy plot - Area of plot excluding the path = [(112 x 78) - (107 x 73)] = 925 m2 = 925 x 10^4 cm^2 Cost on 1000cm2 = 80 paise Total cost =80/100*925*10^4/1000 Rs : 7400
5.
If the perimeter of a rectangular field is 240m and the breadth and length are in the ratio 3:2, what is the area of the field? Let the length of the rectangular field be 3x and breadth be 2x. 2(3x 2x) = 240 10x = 240 .'.x= 24 .'.Required area = 3x * 2x = 3 x 24 x 2 x 24 = 3456 m2
3.SQUARE
Area of square = (side)2 =1/2(diagonal)2 A=a2=1/2d2 *Perimeter of square = 4 x side P = 4a Diagonal of square, d = /2a
EXAMPLES
1.
If the perimeter of a square is 6212cm, find its side P = 4a =6212 a= 6212/4 .'.Side = 1553cm
2.
While measuring the side of a square, an error of 4% in excess is made. Find the percentage of error in the calculated area of the square. 100 cm is read as 104cm .'.A1 = (100 x 100) cm2 and A2 = (104 X 104)cm2 (A2-A1) = (104 x 104)- (100 x 100) =104^2 - 100^2 = (104 100) (104-100) = 204 x 4 = 816 cm2 Percentage error =(816/100*100*100)% =8.16%
3.
75 square stone slabs of equal size were needed to cover a floor area of 147cm2. The length of each stone slab is___ Area of each slab = 147/75 = 1.96 cm2 .'.Length of each slab = /l.96 = 1.4cm
4.PARALLELOGRAM
*Area of parallelogram = base x height A = b x h
5.TRAPEZIUM
*Area of trapezium =1/2(ab)xh where 'a' and 'b' are the length of parallel sides and h is perpendicular distance between a and b. *Perimeter (P) = Sum of all sides
6.RHOMBUS
*Area Of rhombus (A) = Product of diagonals/2 *Perimeter of rhombus = 4a, where 'a' is the length of side.
EXAMPLES
1.
If the base of a parallelogram is 7cm and its area is 42cm2, find its height. A = bxh 42 = 7 x h h=42/7=6 .'.height = 6 cm
2.
The difference between two parallel sides of a trapezium is 10cm. The perpendicular distance between them is 20cm. What will be the lengths of the parallel sides if the area of the trapezium is 800 cm2 Let the two parallel sides be a and b. Given, a - b = 10 ___(i) Now, 1/2(ab)x20 = 800 a b = 80___(ii) (i) and (ii)-> ab = 80 a-b=10 2b = 70 .'.b = 35cm a 35 = 80 .'.a = 45cm .'.Length of the parallel sides are 35cm and 45cm
3.
At the area of the rhombus is 160cm2, find the product of its diagonals. Product of diagonals A= Product of diagonals/2 Product of diagonals = 160 x2 = 320cm
7.CIRCLE
*Area of the circle =?r2 where ?=22/7 =3.14 *Circumference of the circle = 2?r *Length of an arc = 2?r?/360,where ? is the central angle.
EXAMPLES
1.
Find the area of a circle if its circumference is 49 cm. Given, 2?r = 49 .'.r=49/2? Area =?2 =?*(49/2?)^2 =?*49/2?*49/2? =190.98 cm2
2.
The diameter of the driving wheel of a toy is 49cm. How many revolutions per minute must the wheel make inorder to keep a speed of 60 km/hr Distance covered by wheel in 1 minute 60x1000x100/60= 1,00,000 cm Circumference of wheel = 2?r 2* 22/7* 49/2 =154 cm No. of revolutions per minute 1,00,000/154=649
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