Properties and Area of Rhombuses

This video tutorial explains how to calculate the area of a rhombus using the formula involving the product of its diagonals. It provides multiple example problems, demonstrating the use of the Pythagorean theorem to find missing diagonal lengths and solve for the area. The video also covers the concept of using base and height for area calculation in parallelograms, including rhombuses.

What is the formula for calculating the area of a rhombus using its diagonals?

• The product of the diagonals

• One-half the product of the diagonals

• One-half the sum of the diagonals

• The square of one diagonal

If the diagonals of a rhombus intersect at right angles, what property do they exhibit?

• They are congruent

• They are parallel

• They are equal in length

• They bisect each other perpendicularly

In a rhombus, if one diagonal is 20 units and the other is 16 units, what is the area?

• 200 square units

• 240 square units

• 180 square units

• 160 square units

How do you find the missing side of a right triangle in a rhombus using the Pythagorean theorem?

• Add the squares of the two known sides

• Multiply the two known sides

• Divide the hypotenuse by one side

• Subtract the square of one side from the square of the hypotenuse

If a rhombus has a perimeter of 20 units, what is the length of one side?

• 4 units

• 5 units

• 6 units

• 7 units

Given a rhombus with a side length of 5 units and one diagonal of 6 units, what is the length of the other diagonal?

• 5 units

• 10 units

• 8 units

• 4 units

What is the area of a rhombus with a base of 30 units and a height of 15 units?

• 400 square units

• 450 square units

• 300 square units

• 500 square units

Which of the following is true about the area of a parallelogram?

• It is always equal to the square of its base

• It is calculated as base times height

• It is half the product of its diagonals

• It is the sum of its sides

If a rhombus has diagonals of lengths 48 and 14, what is its area?

• 336 square units

• 340 square units

• 350 square units

• 360 square units

What is the relationship between a rhombus and a parallelogram?

• A parallelogram is a type of rhombus

• They are unrelated

• They have no common properties

• A rhombus is a type of parallelogram