Question

4 sayali drew the design shown with sidewalk chalk. the design has four identical shaded parallelograms joined together. each parallelogram has a base of 12 in. and a height of 21 in. what is the area, in square inches, of the unshaded part of sayali’s design? show your work.

Explanation:

Step1: Calculate area of one parallelogram

The area formula for a parallelogram is $A = b\times h$, where $b = 12$ in and $h=21$ in. So $A_1=12\times21 = 252$ in².

Step2: Calculate area of four parallelograms

Since there are 4 identical parallelograms, $A_{shaded}=4\times A_1=4\times252 = 1008$ in².

Step3: Calculate area of the whole rectangle

The rectangle has length $l = 48$ in and width $w = 42$ in. The area formula for a rectangle is $A = l\times w$, so $A_{total}=48\times42=2016$ in².

Step4: Calculate area of the un - shaded part

$A_{unshaded}=A_{total}-A_{shaded}=2016 - 1008=1008$ in².

Answer:

1008 in²