Answer:
203.39 sq meters
Step-by-step explanation:
Start with the rectangles, whose area formula is base * height.
Rectangle S = 10 * 6 = 60 square meters
Rectangle p = 10 * 6 = 60 square meters
A triangle's area formula is (base * height) /2
Triangle R = (10 * 6) /2 = 30 square meters
Now, the diameter of semicircle Q is the same as the hypotenuse of right triangle R. We can find the length of the hypotenuse through the pythagorean theorem.
[tex]10^{2} + 6^{2} = c^{2} = 100 + 36 = 136[/tex]
diameter = [tex]\sqrt{136} = 2\sqrt{34} = approx. 11.66[/tex]
Since the area formula of a circle is [tex]\pi r^{2}[/tex], the area formula for a semicircle is [tex]\frac{(\pi r^{2})}{2}[/tex].
radius = diameter/2 = 11.66/2 = 5.83 meters.
[tex]\frac{(\pi 5.83^{2})}{2} = \frac{33.9889\pi }{2} = 16.99445\pi = 53.39[/tex]
Now, let's add it all together
60 + 60 + 30 + 53.39 = 203.39 square meters. hope this helps!
side note: i am not 100% sure what the rules are regarding rounding irrational numbers during calculations, but what I did was round past the tenth place during calculations to (hopefully) give a more accurate final answer rounded to the tenth place).
