WORKSHEET ON QUADRILATERALS

1. A simple closed shape made up of four line segments is called a _____. 

2. The sum of the measures of interior angles of a quadrilateral is _____. 

3. A parallelogram having all sides equal is called a _____.

4. A quadrilateral having exactly one pair of parallel sides is called a _____.

5. A quadrilateral with right angle at each vertex and having two pairs of equal sides is called a _____.

6. A quadrilateral with right angle at each vertex and having four equal sides is called a _____.

7. A quadrilateral having two pairs of equal and parallel sides is called a _____.

8. If the consecutive sides of a parallelogram are equal, then it is necessarily a _____.

9. Formula for area of a square in terms of the length of each diagonal d is _____.

10. Formula for area of a rhombus when the lengths of two diagonals are d₁ and d₂ is _____.

11. "A quadrilateral has at least one pair of opposite sides congruent" - What type of special quadrilateral can meet the above condition ?

12. When we join the midpoints of the sides of any quadrilateral, what type of special quadrilateral formed ? Explain your answer.   

13. One angle of a quadrilateral is 150° and other three angles are equal. What is the measure of each of these equal angles ?

(a) 75°      (b) 85°        (c) 95°     (d) 70°

14. Two adjacent sides AB and BC of a parallelogram ABCD are in the ratio 5 : 3. If the perimeter is 200 cm, what is the length of AB and BC ?

(a) 25 cm & 50 cm       (b) 40 cm & 37.5 cm

(c) 62.5 cm & 37.5 cm      (d) 60 cm & 62.5 cm

15. Five angles of a hexagon are 150°, 95°, 80°, 135° & 125°. Find the sixth angle.

16. The sum of the angles of a hexagon is_______

(a) 360°      b) 540°     c) 720°     d) 1080°

17. If one angle of a parallelogram is 65o, then the measure of the adjacent angle is

(a) 115°              (b) 65°             (c) 125°             (d) 180o

18. If two adjacent angles of a parallelogram are (5x - 5)° and (10x + 35)°, then the ratio of these angles is

(a) 1 : 3      (b) 2 : 3     (c) 1 : 2      (d) 1 : 4

19.  Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is

(a) 25 cm    (b) 20 cm      (c) 26 cm     (d) 3.5 cm

Answers : 

1. Quadrilaterals

2. 360°

3. Rhombus

4. Trapezoid

5. Rectangle

6. Square

7. Parallelogram

8. Rhombus

9. Area of square = 1/2 ⋅ d²

10. Area of rhombus = 1/2 ⋅ d₁ ⋅ d₂

11. There are many possibilities. 

Parallelogram : Opposite sides are congruent. 

Rhombus : All sides are congruent. 

Rectangle : Opposite sides are congruent. 

Square : All sides are congruent. 

Isosceles Trapezoid : Legs are congruent. 

12. Let E, F, G and H be the midpoints of the sides of the quadrilateral ABCD shown below. 

If we draw AC, the Midsegment Theorem for Triangles says 

FG || AC and EH || AC ----> FG || EH

Similar reasoning shows that 

EF || HG

So, by definition, EFGH is a parallelogram.   

Hence, when the midpoints of the sides of any quadrilateral are joined, the type of special quadrilateral formed is parallelogram. 

13. One angle of a quadrilateral = 150°

Let x be the and other three angles which are equal

Sum of interior angles of quadrilateral = 360

150 + 3x = 360

3x = 360 - 150

3x = 210

x = 210/3

x = 70

So, the equal angles is 70 degree.

14. Sides of parallelogram be 5x and 3x.

Perimeter of parallelogram = 200 cm

5x + 3x + 5x + 3x = 200

16x = 200

x = 200/16

x = 12.5

5x = 5(12.5) ==> 62.5 cm

3x = 3(12.5) ==> 37.5 cm

So, option c is correct.

15. Sum of interior angles polygon = (n - 2) 180

Number of sides of hexagon = 6

= (6 - 2) 180

= 4 x 180

= 720

Let x be the sixth angle.

150 + 95 + 80 + 135 + 125 + x = 720

585 + x = 720

x = 720 - 585

x = 135

So, the sixth angle be 135 degree.

16. Sum of interior angles polygon = (n - 2) 180

Number of sides of hexagon = 6

= (6 - 2) 180

= 4 x 180

= 720

Option c is correct.

17. In a parallelogram, opposite sides will be parallel. Then the parallel sides will make co-interior angles.

Sum of co-interior angles = 180

Let x be the missing angle.

65 + x = 180

x = 180 - 65

x = 115

So, option a is correct.

18. Sum of adjacent angles = 180

5x - 5 + 10x + 35 = 180

15x + 30 = 180

15x = 150

x = 150/15

x = 10

5x - 5 ==> 5(10) - 5 ==> 45

10x + 35 ==> 10(10) + 35 ==> 135

= 45 : 135

= 9 : 27

= 1 : 3

So, option a is correct.

19. Let a and b are the sides and c be the length of diagonal.

c² = a² + b²

a = 10 cm and b = 24 cm

c² = 10² + 24²

= 100 + 576

c² = 676

c = √676

c = 26 cm

So, option c is correct.

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