What is the area of the shaded shape (in red) if all three circles have equal radii of 15 units and are tangent to each other?

Step 1: Inspect the given figure and change the figure according to the given hints in the question.
NOTE :Figure above shows that the centers of the circles make an
equilateral triangle of side 2r where r = 15 (given) is the radius of one circle.
Step 2: Set up a formula to calculate the shaded region
NOTE: The area of the red shape = area of the equilateral triangle - areas
of three congruent sectors (each sector has 60° angle)
Step 3: Find the area of the equilateral triangle
FORMULA: a^2 \frac{\sqrt{3}}{4}
= (2r)^2 \frac{\sqrt{3}}{4}
= (30)^2 \frac{\sqrt{3}}{4}
Step 4: Calculate the areas of three congruent sectors
NOTE: Areas of three congruent sectors = 3 × area of one sector
Area of the sector = \frac{\theta}{360} * \pi r^2
= \frac{60}{360} \pi (15)^2
= \frac{1}{6} 15^2 \pi
Areas of three congruent sectors = 3 * \frac{1}{6} 15^2 \pi
Step 5: Find the shaded region in the figure
The area of the red shape = (30)^2 \frac{\sqrt{3}}{4} - \frac{15^2 \pi}{2}
Step 6: Simplify the equation
NOTE: (30)^2 \frac{\sqrt{3}}{4} - \frac{15^2 \pi}{2}
= [(900 * 0.433 ) - (112.5 * 3.14)
= 389.711 - 353.25
= 36.46 unit^2