Area of Trapezoids and Parallelograms

Front

What is the formula for the area of a trapezoid?

Back

The area of a trapezoid is given by the formula: \( A = \frac{1}{2} (b_1 + b_2) h \), where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides and \( h \) is the height.

Front

What is the formula for the area of a parallelogram?

Back

The area of a parallelogram is given by the formula: \( A = b \times h \), where \( b \) is the base and \( h \) is the height.

Front

How do you find the height of a trapezoid if you know the area and the lengths of the bases?

Back

You can rearrange the trapezoid area formula: \( h = \frac{2A}{b_1 + b_2} \).

Front

What is a parallelogram?

Back

A parallelogram is a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length.

Front

What is a trapezoid?

Back

A trapezoid is a four-sided figure (quadrilateral) with at least one pair of parallel sides.

Front

If a trapezoid has bases of lengths 10 m and 14 m and a height of 5 m, what is its area?

Back

Using the formula: \( A = \frac{1}{2} (10 + 14) \times 5 = 60 \, m^2 \).

Front

If a parallelogram has a base of 8 in and a height of 5 in, what is its area?

Back

Using the formula: \( A = 8 \times 5 = 40 \, in^2 \).

Front

What is the relationship between the area of a rectangle and a parallelogram with the same base and height?

Back

The area of a rectangle is equal to the area of a parallelogram with the same base and height.

Front

How can you determine if a quadrilateral is a trapezoid?

Back

A quadrilateral is a trapezoid if it has at least one pair of parallel sides.

Front

What is the significance of the height in calculating the area of trapezoids and parallelograms?

Back

The height is the perpendicular distance between the bases (for trapezoids) or the base and the opposite side (for parallelograms), and it is crucial for calculating area.