Question

math 6 unit 12 and 13 25-26
10 cm
7 cm
6 cm
james tells lydia to use the length of the slanted sides in order to find the area.
lydia disagrees and says the slanted sides are not important.
who is correct, and what is the area of the poster board? include all necessary math to support your answer.

Explanation:

Step1: Recall parallelogram area formula

The area of a parallelogram is given by \( A = base \times height \), where the base is the length of one of the parallel sides, and the height is the perpendicular distance between the two parallel sides. The slanted side (the side with length 7 cm here) is not the height and is not used in the area formula. So Lydia is correct because we use base and height, not the slanted side.

Step2: Identify base and height

From the diagram, the base of the parallelogram is 10 cm (the horizontal side), and the height is 6 cm (the perpendicular distance between the two horizontal sides).

Step3: Calculate the area

Using the formula \( A = base \times height \), substitute base = 10 cm and height = 6 cm. So \( A = 10 \times 6 = 60 \) square centimeters.

Answer:

Lydia is correct. The area of the poster board (parallelogram) is \( 60 \, \text{cm}^2 \). The calculation is \( \text{Area} = \text{base} \times \text{height} = 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2 \), and the slanted side (7 cm) is not used in the area formula for a parallelogram.