Question

which figure has a greater area? image of two parallelograms: first with base 53 m, height 68 m; second with base 56 m, height 65 m submit

Explanation:

Step1: Calculate area of first parallelogram

The formula for the area of a parallelogram is \( A = base \times height \). For the first figure, base \( b_1 = 53 \, m \) and height \( h_1 = 68 \, m \). So, \( A_1 = 53 \times 68 \).
\( 53\times68 = (50 + 3)\times68 = 50\times68 + 3\times68 = 3400 + 204 = 3604 \, m^2 \)

Step2: Calculate area of second parallelogram

For the second figure, base \( b_2 = 56 \, m \) and height \( h_2 = 65 \, m \). Using the area formula, \( A_2 = 56 \times 65 \).
\( 56\times65 = (50 + 6)\times65 = 50\times65 + 6\times65 = 3250 + 390 = 3640 \, m^2 \)

Step3: Compare the two areas

Compare \( A_1 = 3604 \, m^2 \) and \( A_2 = 3640 \, m^2 \). Since \( 3640>3604 \), the second parallelogram (with base 56 m and height 65 m) has a greater area.

Answer:

The parallelogram with base 56 m and height 65 m (the second figure) has a greater area.