CBSE Class 7 Mathematics Triangles and Its Properties Assignment Set 06

1. In the adjoining figure ABC is a triangle; P is an interior point in it. Three lines are drawn through the point P, parallel to three sides as shown in figure. The triangle is divided into six parts. The areas as 3 smaller triangles are 4, 9 and 16 units, then the area of triangle ABC is…….

(A) 64

(B) 81

(C) 42

(D) 65

Answer : (B)

2. In a triangle ABC, D is the mid-point of AB, E is the mid-point of DB and F is the midpoint of B If the area of DABC is 96, then the area of DAEF is ………..

(A) 16

(B) 24

(C) 32

(D) 36

Answer : (D)

3. In the diagram ABCD is a rectangle with AE = EF = FB, the ratio of the areas of triangle CEF and that of rectangle ABCD is

(A) 1 : 6

(B) 1 : 8

(C) 1 : 9

(D) 1 : 10

Answer : (A)

4. ABCD is a square of area of 4 square units which is divided into 4 non overlapping triangles as shown in figure, then sum of perimeters of the triangles so formed is

(A) 8 ( 2 + √2 )

(C) 4 ( 2 + √2 )

(B) 8 ( 1 + √2 )

(D) 4 ( 1 + √2 )

Answer : (B)

5. In the figure, the area of square ABCD is 4 cm2 and E is midpoint of AB; F, G, H and K are the mid points of DE, CF, DG and CH respectively. The area of triangle KDC is

A) 1/4 cm²

(B) 1/8 cm²

(C) 1/16 cm²

(D) 1/32 cm²

Answer : (B)

6. In the figure ∠D = 90o , AB = 16cm, BC = 12cm and CA = 6cm, then CD is

(A) 13/16 cm

(B) 17/6 cm

(C) 19/6 cm

(D) 18/5 cm

Answer : (C)

7. D ABC is an equilateral triangle, we have BD = EG = DF = DE = EC, then the ratio of the area of the portion to area of D ABC is:

(A) 4/11

(B) 7/9

(C) 5/12

(D) 6/7

Answer : (B)

8.If AP and BP are the bisectors of the angle A and angle B of a parallelogram ABCD, then value of the angle APB is:

(A) 30^o

(B) 45^o

(C) 60^o

(D) 90^o

Answer : (D)

9. In the given figure ABCD is a rectangle and all measurement is in centimeters. Find the area of the shaded region

(A) 240 cm²

(B) 205 cm²

(C) 105 cm²

(D) 95 cm²

Answer : (C)

10. In the given figure, X is point in the interior of square ABCD. AXYZ is also a square. If DY = 3cm, AZ = 2cm then length of BY is:

(A) 5 cm

(B) 6 cm

(C) 7 cm

(D) 8 cm

Answer : (C)

11. ABCD is a quadrilateral in which z/y = y/x = x/w = k and k ϵ z. also {w, x} < 900 and {y, z}> 900, then the difference between the greatest angle and the smallest angle is:

(A) 1280

(B) 1680

(C) 1010

(D) 990

Answer : (B)

12. The fig. below has been obtained by folding a rectangle. The total area of the figure is 144 cm². Had the rectangle not been folded, the current overlapping part would have been a square. What would have been the total area of the original unfolded rectangle?

(A) 162m²

(B) 140cm²

(C) 142mm²

(D) 162cm²

Answer : (D)

13. There are two squares s1 and s2 with areas 8 and 9 square units, respectively s1 is inscribed within s2, with one comes of s1 on each side of s2. The corners of the smaller square divides the sides of the bigger square into two segments, one of the length a and the other of length b, where b>a. a possible value of b a is.

(A) ³ 14 and < 17

(B) >17

(C) ³ 11 and < 14

(D) None of these

Answer : (A)

14. In a square PQRS, A and B are two points on Ps and sR such that PA = 2As and RB = 2Bs. If PQ = 6, the area of the triangle ABQ is.

(A) 5sq. units

(B) 10sq. units

(C) 15sq. units

(D) None of these

Answer : (B)

15. ABC is a triangle in which D, E and F are the mid-point of the sides of AC, BC and AB respectively . what is the ratio of the area of the shaded to the unshaded region in the triangle?

(A) 3 : 2

(B) 1 : 1

(C) 3 : 7

(D) None of these

Answer : (B)

16. The ratio of the area of A to that of C is 16 : 27 and the ratio of B to the area of C is 1 : 3. Find the ratio of the area of A to that of D.

(A) 4 : 5

(B) 5 : 4

(C) 1 : 1

(D) None of these

Answer : (A)

17. In fig., a rectangle is divided into four triangles x, y, z, w. The ratio of area x to area y is 2 : 3 and the ratio of area y to area z is 2 : 3. If area of w is 168cm2. Find the area of the rectangle.

(A) 324cm²

(B) 624cm²

(C) 430cm²

(D) None of these

Answer : (D)

18. In the quadrilateral ABCD ÐA = ÐC = 90^o , AE = 5cm and BE = 12cm and AC = 21 cm. If DF = x, then the value of x is:

(A) 6 (2/3) cm

(B) 10/7 cm

(C) 11 cm

(D) 13 cm

Answer : (A)

19. In the figure, PQ = QR = RS = SP = SQ = 6 cm and PT = RT = 14 cm. The length ST is:

(A) 4 √10 cm

(B) (7√3 - 2) cm

(C) 10 cm

(D) 11 cm

Answer : (C)

20. In the given figure, ABCD is trapezium in which AB ¶ CD and its diagonals intersect at O. If AO = (3x-1) cm, OC = (5x- 3) cm, BO = (2x+1) cm and OD = (6x- 5) cm, find the value of x 

(A) 1/2

(B) 3

(C) 4

(D) 2

Answer : (D)

Fill the Gap

Question. The six elements of a \(\Delta\) are __________ and __________
Answer: Three angles and three sides.

Question. The line segment joining a vertex to the mid point of opposite side is called a __________
Answer: Median

Question. The point of intersection of three altitudes is __________
Answer: Orthocentre

Question. The perpendicular drawn from the vertex to the opposite side is called __________
Answer: Altitude

Question. The point of intersection of three medians is called __________
Answer: Centroid

Question. The number of altitudes of a triangle is __________
Answer: Three

Question. The sum of all angles of a \(\Delta\) is __________
Answer: \(180^\circ\)

Question. In a \(\Delta\), if the length of any two sides are equal then the triangle is __________
Answer: Isosceles

Question. Each angle of an equilateral \(\Delta\) is __________
Answer: \(60^\circ\)

Question. In a \(\Delta\), the exterior angle is equal to sum of __________
Answer: Two interior remote angles.

Question. In a \(\Delta\), the sum of any two sides is __________ than the third side.
Answer: Greater

Question. The difference between the lengths of any two sides is smaller than the __________ of the third side.
Answer: Length.