Question

jacob had a large chocolate cake at his birthday party. after the party, some of the cake was still left.
find the area of the part of the cake that is still left, which is represented by the shaded part of the diagram.
□ in²

Explanation:

Step1: Calculate area of big rectangle

The big rectangle has length 30 in and height 18 in. Area formula: $A = l \times h$. So, $30 \times 18 = 540$ $in^2$.

Step2: Calculate area of unshaded trapezoid

The unshaded part is a trapezoid. The two parallel sides: one is 12 in, the other is $30 - 6 = 24$ in. The height of trapezoid is $18 - 6 = 12$ in. Trapezoid area formula: $A = \frac{(a + b)}{2} \times h$. So, $\frac{(12 + 24)}{2} \times 12 = \frac{36}{2} \times 12 = 18 \times 12 = 216$ $in^2$.

Step3: Subtract unshaded area from big rectangle

Shaded area = Big rectangle area - Unshaded trapezoid area. So, $540 - 216 = 324$ $in^2$.

Answer:

324