Answer:
260 in²
Step-by-step explanation:
The formula for the area of a parallelogram is:
\(\boxed{\begin{array}{l}\underline{\textsf{Area of a parallelogram}}\\\\A=bh\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$b$ is the base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the perpendicular height from the base.}\end{array}}\)
In this case, both the base and the height are 5 inches longer than those in the given parallelogram. Therefore, to find the base (b) and height (h) of the new parallelogram, add 5 inches to each:
\(b = 15 + 5 = 20\; \text{in} \\\\h = 8 + 5 = 13\; \text{in}\)
Now, substitute the values of b and h into the area formula:
\(A=20 \times 13 \\\\ A = 260\; \rm in^2\)
Therefore, the area of a parallelogram that has a base 5 inches longer and a height 5 inches taller than the parallelogram shown is:
\(\LARGE\boxed{\boxed{260 \; \rm in^2}}\)
