Question

marta is making a flag with the given dimensions. the perimeter of the flag is 100 inches.
how much material, in square inches, is needed to make the flag?
square inches
if the material costs $0.15 per square inch, how much will marta spend on materials to make the flag?
$

Explanation:

Step1: Find the third side length

Let the third side be $x$. Perimeter: $18 + 41 + x = 100$
$x = 100 - 18 - 41 = 41$ inches

Step2: Identify triangle type & base

The triangle is isosceles with two sides = 41 in, base = 18 in.

Step3: Calculate height of the triangle

Use Pythagorean theorem: split base into 2 equal parts ($\frac{18}{2}=9$ in).
Height $h = \sqrt{41^2 - 9^2} = \sqrt{1681 - 81} = \sqrt{1600} = 40$ inches

Step4: Compute area of the flag

Area formula: $\frac{1}{2} \times \text{base} \times \text{height}$
$\text{Area} = \frac{1}{2} \times 18 \times 40 = 360$ square inches

Step5: Calculate total material cost

Multiply area by cost per square inch:
$\text{Total Cost} = 360 \times 0.15 = 54$

Answer:

360 square inches
$54$