PERIMETER AND AREA OF PLANE FIGURES
1) Find the area of a triangle with base 24cm and height 15 cm.
2) The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs 38 per hectare is Rs 513, find the base and height.
3) Find the area of a triangle whose sides are 42cm, 34cm and 20 cm. Hence, find the height corresponding to the longest side.
4) Calculate the area of an equilateral triangle of side 12 cm, correct to two decimal places.
5) Calculate the area of an equilateral triangle whose height is 6cm. (Take √3= 1.73).
6) The perimeter of an isosceles triangle is 42 cm and base is 3/2 times each of the equal sides.
7) The base of an isosceles triangle is 24cm and its area is 192 cm². Find its perimeter.
8) The difference between the sides of a right angled triangle containing the right angle is 7cm and its area is 60 cm². Calculate the perimeter of the triangle.
MENSURATION (RECTANGLE)
1) The perimeter of a rectangular plot is 120m. If the length of the plot is twice its width, find the area of the plot. 800m²
2) How many square tiles of side 20cm will be needed to pave a footpath which is 2 meters wide and surrounds a rectangular plot 40m long and 22m wide? 6600
3) The area of a square plot is 1764m². Find the length of its one side and one diagonal. 42, 59.39m
4) Two adjacent sides of a parallelogram are 24cm and 18cm. If the distance between the longer sides is 12cm, find the distance between shorter sides. 16cm
5) If the length of a rectangle is increased by 10cm and breadth is decreased by 5cm, the area is unaltered. If the length is decreased by 5cm and breadth is increased by 4cm, even then the area is unaltered. Find the dimensions of the rectangle. 30,20
6) The sides of a square exceeds the side of another square by 3cm and the sum of the areas of the two squares is 549 cm². Find the perimeters of the squares. 60,72
7) If the sides of a square are lengthened by 3cm, the area becomes 121 cm². Find the perimeter of the original square. 32cm
TRIANGLE AND RECTANGULE/SQUARE (Mixed)
1) A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 15, 14 and 13cm and the parallelogram stands on the base 15cm, find the height of the parallelogram. 5.6cm
2) A kite in the shape of a square with diagonal 32cm and an isosceles triangle of base 8cm and sides 6cm each is to be made of three different shades as shown in the figure. How much paper of each shade has been used in it ? 17.9cm² (app)
3) ABCD is a square with sides of length of 6cm. Find point M on BC such that area of ∆ ABM: area of trapezium ADCM = 1:3.
4) In the adjoining figure, ABCD is a square. E is a point DC such that area of ∆ AED: area of the trapezium ABCE = 1:5, find the ratio of the perimeters of ∆ AED and trapezium ABCE. (4+ √10): (8+ √10)
PERIMETER AND AREA OF QUADRILATERAL
1) In a four sided field, the longer diagonal is 108m. The lengths of the perpendiculars from the opposite vertices upon this diagonal are 17.6 m and 12.5 m respectively. Find the area of the field.
2) Find the area of a quadrilateral whose sides are 9m, 40m, 28m and 15m respectively and the angle between first two sides is a right angle.
3) The length of the rectangular plot is twice its breath. If the perimeter of the plot is 270 m, find its area.
4) Find the area of a rectangular plot of land one of whose sides measure 35m and the length of the diagonal 37 m.
5) A rectangular carpet has an area of 60m². if its diagonal and longer side together equal 5 times the shorter side, find the length of the carpet .
6) The length of the diagonal of a square is 36 cm. Find
a) the area of the square
b) its perimeter upto 2 decimals places.
7) Find the area of a parallelogram one of whose sides is 34 cm and the corresponding height is 8cm.
8) Two adjacent sides of a parallelogram are 24cm and 18 cm. If the distance between the longer sides is 12cm, find the distance between the shorter sides.
9) The diagonals of a rhombus are 30cm and 16 cm.
a) Find the area of the rhombus .
b) the perimeter of the Rhombus.
10) Find the area of a trapezium whose parallel sides are 25cm and 18 cm and the distance between them is 8 cm.
11) Find the area of a trapezium ABCD in which AB || DC, AB= 77cm, BC= 25cm, CD= 60cm and DA= 26cm.
12) The length and breadth of a rectangular grassy plot are in the ratio 7:4. A path 4 m wide running all around outside it has an area of 416m². Find the dimensions of the grassy plot.
13) A rectangular lawn 60m by 40m has two roads, each 5m wide, running in the middle of it, one parallel to length and the other parallel to breadth. Find the cost of the gravelling them at Rs 3.60 per m².
14) if the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 m². If the length is increased by 1 m and breadth is decreased by 1m, then the area is decrease by 7 m². Find the perimeter of the floor.
PAPER- 2
1) If (5+ 2√3)/(7+ 4√3)= a - b √3, find a, b.
2) The difference between the compound intrest and the simple intrest on Rs42000 for two years is Rs105 at the same rate of interest per annum. Find
a) the rate of interest
b) the compound intrest earned in the second year.
3) If x= 2y+6, then find the value of x³- 8y³- 36xy - 216.
4) If a+ b= 10 and a²+ b²= 58, find the value of a³+ b³.
5) factorise: 8x³- (2x - y)³.
6) Solve: 83x - 67y =383; 67x - 83y = 367.
7) A number of three digits has the hundred digit 4 times the unit digit and the sum of three digits is 14. If the three digits are written in the reverse order, the value of the number is decreased by 594. Find the number.
8) (7²ⁿ⁺³ - (49)ⁿ⁺²)/((343)ⁿ⁺¹)²⁾³. Evaluate
9) Solve: 5²ˣ⁺³= 1.
10) Solve: logₓ25 - logₓ5 + logₓ(1/125)= 2.
11) In the figure 
AB= PQ, BR= CQ, AB perpendicular to BC and PQ perpendicular to RQ. Prove AC = PR.
12) ABC is an isosceles triangle with AB= AC= 12cm, and BC= 8cm, find the altitude on BC and hence find its area.
13) In the figure 
Find the angles of the parallelogram.
14) In a circle of radius 5cm, AB and CD are two parallel chords of length 8cm and 6cm respectively. Find the distance between the chords, if they are on
a) the same side of the centre
b) the opposite sides of the centre.
15)
Find the area of the shaded part
16) ABCD is a square with sides of length of 6cm. Find point M on BC such that area of ∆ABM: area of trap ADCM= 1: 3.
Paper- 1
1) Rationalize: 4/(√5- √3).
2) Expand: (3a + 5b)².
3) If x - 1/2x = 3, find the value of
a) x²+ 1/4x²
b) x⁴+ 1/16x⁴.
4) If (x²+1)/x = 5/2, find the value of
a) x - 1/x.
b) x³- 1/x³.
5) Evaluate: (3a²- b²)(2a²+ 5b²).
6) Factorise:
a) x²+ 1/x²+ 2 - 2x - 2/x.
b) (x²+ y²- z²)²- 4x²y².
c) x²+ 11x +30.
7) Solve:
a) 5/x + 6y = 13, 3/x + 4y =7.
b) 5x + 4y - 4= 0, x - 20= 12y.
8)a) The sum of two numbers is 69 and their difference is 17. Find the numbers.
b) If 2 is added to each of the two given numbers, then their ratio becomes 1:2. However, if 4 is substracted from each of the given numbers, the ratio becomes 5:11. Find the numbers.
9) If 2ˣ = 3ʸ= 12ᶻ, show that: 1/z = 1/y + 2/x.
10) Evaluate: log₉27= 2x +3.
11) In a ∆ ABC, angle A= 110° and angle B+ angle C= 115°. Calculate Angle A, B, C.
12) In ∆ ABC, if angle A - angle B= 29° and angle A - angle C = 40°, find the angles A,B, C.
13) Show that the perpendicular drawn from the extremities of the base of an isosceles triangle to the opposite sides are equal.
14) Prove that the figure obtained by joining the midpoints of the adjacent sides of a quadrilateral is a parallelogram.
15) The sides of a right triangle containing the right angle are 5x cm and 3x -1 cm. If the area of the triangle be 60cm², calculate the length of the sides of the triangle.
16) If one angle of a parallelogram is 90°, show that each of its angles measures 90°.
17) Find the area of a trapezium whose parallel sides measure 10cm and 8 cm respectively and the distance between these sides is 6 cm.
18) If θ is an acute angle such that sinθ= √3/2, then find the value of (cosecθ + cotθ).
19) If A= 60° verify that cosec²A - cot²A = 1.
20) Show that tan35 tan 40 tan 45 tan 50 tan 55=1.
21) Find the area of a triangle with base 24cm and height 15cm.
22) The length of a rectangle plot is twice its breadth. If the perimeter of the plot is 270m, find its area.
23) The surface area of a cube is 1536 cm², find
a) the length of its edge.
b) its volume.
c) the volume of its material whose thickness is 5 mm.
24) Show that A(2,-2), B(8,4) and C(5,7) are collinear.
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