### MCQ on Areas of parallelograms and Triangles

**Ques.** A parallelogram *ABCD* and a rectangle *ABPQ* are on the same base *AB* and between the same parallels *AB* and *CQ*. If *AB* = 8 cm and *AQ = *6 cm, find the area of ||gm *ABCD*.

(a) 52 cm^{2}

(b) 46 cm^{2}

(c) 48 cm^{2}

(d) 58 cm^{2}

**Ques.** In the given figure, PQS = SRQ, QPR = SRQ, U is a point on QR such that QPU = 300, then QUP is

(a) 40^{o}

(b) 50^{o}

(c) 60^{o}

(d) 70^{o}

**Ques. **One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.

(a) 120 m^{2}

(b) 80 m^{2}

(c) 90 m^{2}

(d) 70 m^{2}

**Ques.** In a ABC, the medians AD, BE and CF intersects at G. If AD = 7.2 cm, then AG is

(a) 4.8 cm

(b) 2.4 cm

(c) 3.6 cm

(d) 1.7 cm

**Ques.** The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

(a) |m + n| / (m – n)^{2}

(b) 2 / | m + n |

(c) 1 / | m + n|

(d) 1 / |m – n|

**Ques. **In a parallelogram ABCD ∠D = 60^{o} then the measurement of ∠A

(a) 120^{o}

(b) 65^{o}

(c) 90^{o}

(d) 75^{o}

**Ques.** In the figure below, PQ!!SR, If x = and y = , then the values of x, y, z are

(a) 36, 60, 84

(b) 45, 25, 110

(c) 46, 50, 84

(d) None of these

**Ques. **Find the area of a square, one of whose diagonals is 3.8 m long.

(a) 8.25 m^{2}

(b) 8.22 m^{2}

(c) 7.25 m^{2}

(d) 7.22 m^{2}

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**Ques. **In **△**ABC, AD is a median and P is a point is AD such that AP : PD = 1 : 2 then the area of **△**ABP =

(a) 1/3 x Area of **△**ABC

(b) 2/3 x Area of **△**ABC

(c) 1/3 x Area of **△**ABC

(d) 1/6 x Area of **△**ABC

**Ques.** Medians BD and CE of triangle ABC are perpendicular, BD = 8 and CE = 12. The area of triangle ABC is

(a) 24

(b) 32

(c) 48

(d) 64

**Ques. **Find the area a rhombus, the lengths of whose diagonals are 16 cm and 24 cm respectively.

(a) 92 cm^{2}

(b) 192 cm^{2}

(c) 108 cm^{2}

(d) 168 cm^{2}

**Ques. **Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of $12.40 per square metre.

(a) 1944.40

(b) 1934.40

(c) 1930.40

(d) 1940.40

**Ques.** If x^{2} + y^{2} + z^{2} = xy + yz + zx, then the triangle is

(a) Isosceles

(b) right angled

(c) equilateral

(d) scalene

**Ques.** The resultant of three forces represented in magnitude and direction by the sides of a triangle *ABC* taken in order with *BC* = 5 *cm*, *CA* = 5 *cm*, and *AB* = 8 *cm*, is a couple of moment

(a) 12 unit

(b) 24 unit

(c) 36 unit

(d) 16 unit

**Ques. **The sum of the interior angles of polygon is three times the sum of its exterior angles. Then numbers of sides in polygon is

(a) 6

(b) 7

(c) 8

(d) 9

**Ques.** In the given figure, ABC is a triangle and D is a point on AC, given that ∠ABC = 65^{o}, ∠BDC = 2∠ABD and ∠BDA = 3∠DBC. Then ∠BCD is

(a) 100^{o}

(b) 105^{o}

(c) 110^{o}

(d) 120^{o}

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**Ques. **A room is half as long again as it is broad. The cost of carpeting the at $5 per sq. m is $270 and the cost of papering the four walls at $10 per m2 is $1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.

(a) 19 m

(b) 13 m

(c) 7 m

(d) 6 m

**Ques.** In the given triangle DEF, points A,B and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. If angle D = 40 degrees, then the angle of ACB in degrees is

(a) 140

(b) 70

(c) 100

(d) None of these

**Ques. ***ABCD* is parallelogram. If *AB* = 3.6 cm and altitude corresponding to sides *AB* and *AD* are respectively 5 cm and 4 cm, then *AD* will be

(a) 5.5 cm

(b) 3.5 cm

(c) 2.5 cm

(d) 4.5 cm

**Que.** ABCD is a parallelogram, if the two diagonals are equal, then the measure of ABC is

(a) 90^{o}

(b) 45^{o}

(c) 60^{o}

(d) 120^{o}

**Ques.** In the figure (not drawn to scale) given below,if AD = CD = BC, and , then ∠DBC is

(a) 32^{o}

(b) 84^{o}

(c) 64^{o}

(d) Cannot be determined

**Ques.** If the equations of opposite sides of a parallelogram are x^{2} – 7x + 6 = 0 and y^{2} – 14y + 40 = 0, then the equation of its one diagonal is

(a) 6x + 5y + 14 = 0

(b) 6x – 5y + 14 = 0

(c) 5x + 6y + 14 = 0

(d) 5x – 6y + 14 = 0

**Ques.** In the following triangle ABC, the angles x, y, z are

(a) 40^{o}, 110^{o}, 30^{o}

(b) 100^{o}, 30^{o}, 50^{o}

(c) 50^{o}, 70^{o}, 60^{o}

(d) 80^{o}, 60^{o}, 30^{o}

**Ques.** The sides of a triangle are in the ratio 3 : 5 : 7 and its perimeter is 30 cm. The length of the greatest side of the triangle in cm is

(a) 6

(b) 10

(c) 14

(d) 16

**Ques. **If each side of a square is increased by 25%, find the percentage change in its area.

(a) 47.25%

(b) 66.25%

(c) 62.25%

(d) 56.25%

**Ques.** In the figure below, CF and DG are the bisectors of ∠BCD and ∠BDC respectively. then ∠GFC is

(a) 50^{o}

(b) 60^{o}

(c) 65^{o}

(d) 75^{o}

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**Ques. **In **△**ABC if D is a point in BC and divides it the ratio 3 : 5 i.e., if BD : DC = 3 : 5 then, ar (**△**ADC) : ar(**△**ABC) = ?

(a) 3 : 5

(b) 3 : 8

(c) 5 : 8

(d) 8 : 3

**Ques. **The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

(a) 32 cm

(b) 28 cm

(c) 24 cm

(d) 20 cm

**Ques.** In the given figure, ∠B = ∠C = 65° and ∠D = 30°, then

(a) BC < CA < CD

(b) BC < CA, CA > CD

(c) BC > CA > CD

(d) BC > CA, CA < CD

**Ques. **How many triangles can be drawn by means of 9 non-collinear points

(a) 84

(b) 72

(c) 144

(d) 126

**Ques.** The angle between the bisectors of the two acute angles of a right angle triangle is

(a) 120^{o}

(b) 135^{o}

(c) 112½^{o}

(d) 90^{o}

**Ques. **Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.

(a) 30 cm^{2}

(b) 25 cm^{2}

(c) 35 cm^{2}

(d) 20 cm^{2}

**Ques.** In the figure the measure of ∠A is

(a) 95°

(b) 105°

(c) 65°

(d) 35°

**Ques. **Find the area of trapezium whose parallel sides are 8 cm and 6 cm respectively and the distance between these sides is 8 cm.

(a) 56 cm^{2}

(b) 52 cm^{2}

(c) 58 cm^{2}

(d) 54 cm^{2}

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**Ques.** The area of trapezium whose parallel sides are 9cm and 6cm respectively and distance between these sides is 8 cm will be

(a) 50 cm^{2}

(b) 60 cm^{2}

(c) 70 cm^{2}

(d) 80 cm^{2}

**Ques.** If ∠EFC = y°, ∠FEB = x°, ∠ACD = 128°, AB = AE, ABEF then angles x° and y° are

(a) x = 58° ; y = 110°

(b) x = 110° ; y = 58°

(c) x = 110° ; y = 180°

(d) x = 68° ; y = 110°

**Ques. **Area of rhombus whose diagonals are 16cm and 24cm will be

(a) 182 cm^{2}

(b) 202 cm^{2}

(c) 92 cm^{2}

(d) 192 cm^{2}

**Ques. **A room 5m 55cm long and 3m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.

(a) 173

(b) 174

(c) 175

(d) 176

**Ques.** If ∠B < ∠A and ∠C <∠D, then

(a) AD > BC

(b) AD < BC

(c) AD = BC

(d) AD = CD

**Ques. **If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.

(a) 100 cm^{2}

(b) 120 cm^{2}

(c) 80 cm^{2}

(d) 150 cm^{2}

**Question:** The number of triangles that can be formed by 5 points in a line and 3 points on a parallel line, is

(a) ^{8}C_{3}

(b) ^{8}C_{3} – ^{5}C_{3}

(c) ^{8}C_{3} – ^{5}C_{3} – 1

(d) none of these

**Ques.** If AB = 13x – 50 ; AE = 20 – 11y ; DF = 50 – 11x ; CF = 13y – 24, AB = AE, FC = DF, then

(a) x > y

(b) x = y

(c) x < y

(d) x > y

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**Ques. **Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq. metres.

(a) 58 m

(b) 48 m

(c) 56 m

(d) 52 m

**Ques.** In a parallelogram ABCD, AB = 8 cm. The altitudes corresponding to sides AB and AD are respectively 4 m and 5 cm. Find AD.

(a) 6.4 cm

(b) 6.6 cm

(c) 6.5 cm

(d) 6.2 cm

**Ques. **If the length of a certain rectangle is decreased by 4 cms and the width is increased by 3 cms, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

(a) 50 cms

(b) 51 cms

(c) 52 cms

(d) 53 cms

**Ques. **The difference between two parallel sides of a trapezium is 4 cms. perpendicular distance between them is 19 cms. If the area of the trapezium is 475 find the lengths of the parallel sides*.*

(a) 26 cms, 25 cms

(b) 27 cms, 23 cms

(c) 28 cms, 25 cms

(d) 25 cms, 22 cms

**Ques. **In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

(a) 6 : 7

(b) 16 : 9

(c) 4 : 5

(d) 16 : 15

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**Ques. **The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.

(a) 15.5 cm

(b) 17 cm

(c) 22 cm

(d) 20 cm

**Ques. **The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.

(a) 3 : 4

(b) 4 : 5

(c) 4 : 25

(d) 6 : 11

**Ques. **Find the length of the altitude of an equilateral triangle of side 3√3 cm.

(a) 5.5 cms

(b) 6.5 cms

(c) 4.5 cms

(d) 7.5 cms

**Ques. **In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements*.*

(a) 0.8%

(b) 1.8%

(c) 1.2%

(d) 1.0%

**Ques. **Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.

(a) 78 cm^{2}

(b) 86 cm^{2}

(c) 84 cm^{2}

(d) 82 cm^{2}

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**Ques. **The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height.

(a) 8 cms

(b) 6 cms

(c) 9 cms

(d) 5 cms

**Ques. **A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 cents per sq. metre.

(a) $670

(b) $680

(c) $640

(d) $650