Quadrilateral Worksheets

**Page 1**

1.

Which quadrilateral has two pairs of parallel sides and does not have a right angle?

a. | parallelogram | ||

b. | rectangle | ||

c. | triangle | ||

d. | square |

Angles in a square and a rectangle are right angles.

Parallelogram is the quadrilateral that has two pairs of parallel sides and does not have right angles.

Correct answer : (1)

2.

Which name does not suit the quadrilateral RSTU?

a. | Trapezoid | ||

b. | Rectangle | ||

c. | Rhombus | ||

d. | None of the above |

So, it can be a rectangle or a rhombus.

A trapezoid has only one pair of parallel sides.

So, the quadrilateral RSTU cannot be a trapezoid.

Correct answer : (1)

3.

Which of the following statements is/are correct?

1. In a rhombus and a square, the diagonals bisect each other.

2. In a rhombus and a square, the diagonals are perpendicular.

3. All the sides in a rhombus and a square are equal.

4. Rhombus and square have equal measures of their diagonals.

1. In a rhombus and a square, the diagonals bisect each other.

2. In a rhombus and a square, the diagonals are perpendicular.

3. All the sides in a rhombus and a square are equal.

4. Rhombus and square have equal measures of their diagonals.

a. | (1), (2) and (3) | ||

b. | (2) and (3) | ||

c. | Only (4) | ||

d. | All the statements |

Both in rhombus and square, the diagonals are perpendicular to each other. So, statement 2 is correct.

All sides of rhombus and square are equal. So, statement 3 is correct.

The measures of diagonals of a square are equal, but the measures of diagonals of a rhombus need not be equal. So, statement 4 is incorrect.

Correct answer : (1)

4.

Which of the following statements is/are incorrect?

1. A square is a rhombus but a rhombus is not a square.

2. Both square and rhombus have four congruent sides.

3. Diagonals bisect each other at right angles in both square and rhombus.

4. Measures of diagonals are equal in both square and rhombus.

1. A square is a rhombus but a rhombus is not a square.

2. Both square and rhombus have four congruent sides.

3. Diagonals bisect each other at right angles in both square and rhombus.

4. Measures of diagonals are equal in both square and rhombus.

a. | Only (4) | ||

b. | (1) and (2) | ||

c. | (2) and (3) | ||

d. | (3) and (4) |

Both square and rhombus have four congruent sides. So, statement 2 is correct.

In both rhombus and square, the diagonals bisect each other at right angles. So, statement 3 is correct.

The measures of diagonals in a square are equal, but not in a rhombus. So, statement 4 is incorrect.

Correct answer : (1)

5.

Which among the following statements is/are correct for a rhombus and a rectangle?

1. The diagonals bisect each other at right angles.

2. The opposite angles are equal.

3. The measures of diagonals are equal.

4. All sides are equal.

1. The diagonals bisect each other at right angles.

2. The opposite angles are equal.

3. The measures of diagonals are equal.

4. All sides are equal.

a. | 1 and 2 | ||

b. | Only 2 | ||

c. | 1 and 4 | ||

d. | 3 and 4 |

Opposite angles are equal for both rhombus and rectangle. So, statement 2 is correct.

The measure of diagonals of a rectangle are equal, but the measures of diagonals of a rhombus need not be equal. So, statement 3 is not correct.

All sides of a rhombus are equal, but only opposite sides of a rectangle are equal. So, statement 4 is incorrect.

Correct answer : (2)

6.

Three angles of a quadrilateral are 109^{o}, 71^{o}, and 99^{o}. What is the measure of the fourth angle?

a. | 279 ^{o} | ||

b. | 109 ^{o} | ||

c. | 69.75 ^{o} | ||

d. | 81 ^{o} |

Let

[Subtract 279 from both sides.]

So, the measure of the fourth angle is 81

Correct answer : (4)

7.

The measures of all the sides of the figure shown are equal and the adjacent sides are perpendicular to each other. Name the figure.

a. | Trapezoid | ||

b. | Rectangle | ||

c. | Square | ||

d. | Rhombus |

So, the quadrilateral is a square.

Correct answer : (3)

8.

a. | 60 ^{o} | ||

b. | 90 ^{o} | ||

c. | 45 ^{o} | ||

d. | 120 ^{o} |

Diagonals of a square bisect each other at right angles.

So,

Correct answer : (2)

9.

a. | 42 ^{o} | ||

b. | 144 ^{o} | ||

c. | 92 ^{o} | ||

d. | 72 ^{o} |

[Substitute and simplify.]

Correct answer : (4)

10.

a. | 42 square units | ||

b. | 37 square units | ||

c. | 47 square units | ||

d. | 28 square units |

Area of the parallelogram = 56 square units

Area of ΔDOC = one fourth of area of ABCD =

Area of the shaded region = the area of the parallelogram - the area of ΔDOC = 56 - 14 = 42 square units

[Substitute and simplify.]

The area of the shaded region is 42 square units.

Correct answer : (1)