Exploring Area of Parallelograms and Triangles

What is the primary difference between area and perimeter?

• Area is only applicable to circles, while perimeter is applicable to all shapes.

• Area and perimeter are the same for all shapes.

• Area measures the space inside a shape, while perimeter measures the distance around a shape.

• Area measures the distance around a shape, while perimeter measures the space inside a shape.

How do you find the area of a figure using the concept of area addition?

• By using the Pythagorean theorem.

• By measuring the perimeter and dividing by two.

• By breaking the figure into smaller non-overlapping parts and summing their areas.

• By multiplying the length and width of the figure.

What is the formula for the area of a parallelogram?

• Base times height

• Side squared

• Radius squared times pi

• Length times width

Why must the base and height of a parallelogram be perpendicular?

• Because they are parallel to each other.

• Because they are the same as the sides of the parallelogram.

• Because they form a right angle.

• Because they are always equal in length.

In the given example, what is the height of the parallelogram if the base is 32 inches and the hypotenuse of the right triangle is 20 inches?

• 12 inches

• 16 inches

• 32 inches

• 20 inches

How do you find the perimeter of a parallelogram?

• By adding up the lengths of all sides.

• By multiplying the base and height.

• By dividing the area by the base.

• By using the Pythagorean theorem.

When the height of a parallelogram is outside the shape, how is it determined?

• By using the area formula directly.

• By measuring the slanted side.

• By extending the base and measuring the perpendicular distance.

• By using the perimeter formula.

How can trigonometry be used to find the height of a parallelogram?

• By using the cosine of the given angle and the base.

• By using the Pythagorean theorem.

• By using the sine of the given angle and the hypotenuse.

• By using the tangent of the given angle and the perimeter.

What is the formula for the area of a triangle?

• Base times height

• One-half base times height

• Side squared

• Length times width

If one board is 3 feet long and one bag of sand fills 9 square feet, how many bags of sand are needed to fill a triangular sandbox with an area of 54 square feet?

• 5 bags

• 6 bags

• 7 bags

• 4 bags