Mathematics

Parallelogram Properties and Area

93 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

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

What is the name of the algorithm that finds the volume of a parallelepiped?

  1. Cavalieri's principle

  2. Pythagorean theorem

  3. Heron's formula

  4. Euler's formula
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cavalieri's principle is an algorithm that finds the volume of a parallelepiped in $O(1)$ time.

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).