Area and Properties of Rhombuses

The video tutorial explains the properties of a rhombus, a shape with four equal sides and opposite sides parallel. It covers three methods to calculate the area of a rhombus: using diagonals, using base and height, and using trigonometry. The diagonal method involves measuring the diagonals and dividing the product by two. The base and height method requires measuring the base and perpendicular height. The trigonometry method uses the sine of an angle and the length of a side. Each method is illustrated with examples.

What is a defining characteristic of a rhombus?

• It is always a square.

• It has two pairs of parallel sides.

• All sides are of equal length.

• It has four right angles.

How does a rhombus differ from a square?

• A square has no parallel sides.

• A square is not a type of rhombus.

• A rhombus can have angles other than 90 degrees.

• A rhombus has unequal sides.

What is the first step in calculating the area of a rhombus using its diagonals?

• Find the base length.

• Calculate the height.

• Measure the diagonals.

• Measure the perimeter.

If a rhombus has diagonals measuring 10 cm and 6 cm, what is its area?

• 45 cm²

• 15 cm²

• 60 cm²

• 30 cm²

What is the formula for finding the area of a rhombus using its base and height?

• Base × Height × 2

• Base × Height ÷ 2

• Base + Height

• Base × Height

If a rhombus has a base of 12 cm and a height of 8 cm, what is its area?

• 24 cm²

• 60 cm²

• 96 cm²

• 48 cm²

Which trigonometric function is used to calculate the area of a rhombus when one side and an angle are known?

• Secant

• Tangent

• Sine

• Cosine

If a rhombus has a side length of 6 cm and a 45-degree angle, what is the approximate area?

• 18 cm²

• 36 cm²

• 30.63 cm²

• 24 cm²

What is the result of multiplying the side length squared by the sine of the angle in a rhombus?

• The height

• The area

• The perimeter

• The diagonal length

Which of the following is NOT a method to calculate the area of a rhombus?

• Using trigonometry

• Using perimeter

• Using base and height

• Using diagonals