Answer:
39.8 cm^2
Step-by-step explanation:
area of triangle
base = 5 cm
height = 12 cm
are of triangle = base *height / 2
=5*12/2
=60/2
30 cm^2
area of semi circle
diamtere = 5
radius = diameter/2
=5/2
=2.5
area of semi circle = πr^2/2
=3.14*2.5^2/2
=19.625/2
=9.8125 cm^2
are of the figure = are of triangle + area of semicircle
=30 + 9.8125 cm^2
=39.8125 cm^2
=39.8 cm^2 (after converting to the nearest tenth)
From the shaded diagram, Raphael will need 3 of the 6 equal portions, or exactly 1/2 of the area of the circle. Given a radius of 12 ft, knowing that the area of any given circle is

, and knowing that the area of the fabric needs to be half of the total area, we can set up the equation for the area of the fabric

:

Simplifying, we find that the area of the fabric is exactly

ft.² Using the approximation of 3.14 for π, we get an area of approximately

ft² of fabric.
Conversion.
1 yard = 3 feet
So the fabric has 2 yards. Then the size of the patch is 1/4 foot.
So the number of patches that Marcus used is..
= 3 * 2
= 6 / (1/4)
= 24 patches.
So a total of 24 patches Marcus used.