Mathematics

Parallelogram Properties and Area

86 Questions

Parallelogram properties and area questions test the ability to calculate dimensions using base and height ratios. Problems also cover diagonal properties and internal angles. These geometry concepts regularly appear in quantitative aptitude sections of various exams.

Area calculationBase and height ratiosDiagonal propertiesInterior anglesGeometric theorems

Parallelogram Properties and Area Questions

Multiple choice

Which of the following quadrilaterals has two congruent diagonals?

  1. Rectangle

  2. Square

  3. Rhombus

  4. Parallelogram
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A rhombus is a quadrilateral with two congruent diagonals.

Multiple choice

Which of the following quadrilaterals has four equal angles?

  1. Rectangle

  2. Square

  3. Rhombus

  4. Parallelogram
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A square is a quadrilateral with four equal angles.

Multiple choice

Which of the following quadrilaterals has four congruent sides and four right angles?

  1. Rectangle

  2. Square

  3. Rhombus

  4. Parallelogram
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A square is a quadrilateral with four congruent sides and four right angles.

Multiple choice

What is the name of the theorem that states that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Brahmagupta's Identity
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Brahmagupta's Identity states that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides. This theorem is attributed to Indian mathematicians.

Multiple choice

In a parallelogram, opposite sides are:

  1. Congruent

  2. Parallel

  3. Perpendicular
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a parallelogram, opposite sides are congruent.

Multiple choice

What is the name of the theorem that states that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Parallelogram law
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The parallelogram law states that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Multiple choice

What is the name of the theorem that states that the sum of the squares of the two diagonals of a parallelogram is equal to the sum of the squares of its four sides?

  1. Pythagorean theorem

  2. Triangle inequality theorem

  3. Euler's theorem

  4. Brahmagupta's theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Brahmagupta's theorem states that the sum of the squares of the two diagonals of a parallelogram is equal to the sum of the squares of its four sides. This theorem is named after Brahmagupta, who first discovered it in the 7th century AD.

Multiple choice

What is the name of the theorem that states that the diagonals of a rhombus bisect each other at right angles?

  1. Heron's formula

  2. Pythagorean theorem

  3. Brahmagupta's theorem

  4. Rhombus diagonal theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The rhombus diagonal theorem is a result in geometry that establishes a relationship between the diagonals of a rhombus.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 10 cm and the side AC is 6 cm. If triangle PQR is similar to triangle ABC, where PQ is 15 cm, what is the length of QR?

  1. 9 cm

  2. 12 cm

  3. 15 cm

  4. 18 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 10/15 = 6/QR. Solving for QR, we get QR = 12 cm.

Multiple choice

What is the formula for the area of a parallelogram, as given by Bhaskara II?

  1. $\text{Area} = \text{base} \times \text{height}$
  2. $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
  3. $\text{Area} = 2 \times \text{base} \times \text{height}$
  4. $\text{Area} = \frac{1}{4} \times \text{base} \times \text{height}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara II's formula for the area of a parallelogram is $\text{Area} = \text{base} \times \text{height}$. This formula is still used today in geometry.

Multiple choice

Find the area of the parallelogram formed by the vectors (\vec{A} = 2\hat{i} + 3\hat{j}) and (\vec{B} = 4\hat{i} - \hat{j}).

  1. 6

  2. 10

  3. 14

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of the parallelogram formed by two vectors is given by the formula (A = |\vec{A} \times \vec{B}|). Substituting the values of the vectors, we get (A = |\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 3 & 0 \ 4 & -1 & 0 \end{vmatrix}| = |\langle 3, 8, -10 \rangle| = \sqrt{3^2 + 8^2 + (-10)^2} = \sqrt{9 + 64 + 100} = \sqrt{173} = 14).