19a. Well, we can start off by finding the perimeter of the quadrilateral and then move on to the semi-circle. We know that the radius of the semi-circle is 5, right? Therefore, we can also say that the diameter is 10, since 5*2 is 10.
Sides of the quadrilateral: 11.2, 10, 15, 10
Add them all up:
11.2+10+15+10 = 46.2
Now for the semicircle.
The perimeter of a normal is 2πr right? Essentially, we just need to change that formula up a bit so it looks like this:
<u>πr + d</u>
It may seem a bit confusing, but you can't just divide the normal equation by 2. You have to "walk" across the semi-circle, too! This means that we also have to add the diameter. (We already know it's 10, because of the first question)
So, input all the terms:
π(5) + 10 = 25.7079 (I don't know how specific it has to be)
Add the perimeter of the quad and the semi-circle:
25.7079+46.2 = <u>71.9079 yards</u>
<u></u>
19b. First, let's find the area of the quad.
The quadrilateral is essentially a triangle and a square shoved togther, so let's split the quadrilateral up and combine the areas later.
15-10 = 5, right? This means that the height of the triangle will be 5, and the width will be 10 (diameter of the circle!)
1/2*5*10 = 25 yd^2
Now for the square:
The width and the length are both ten. 10*10 = 100 yd^2
100 + 25 = 125 yd^2
Now for the semi-circle (Almost done!)
The formula for the area of a circle is πr^2, so we just have to divide it by 2 (no need to add the diameter, we don't have to "walk" along it)
The new formula we get it πr^2/2
Input values:
π*5^2/2 = 25π/2 = 39.2699
Add all the values:
125 + 39.2699 = 164.2699 yds^2
TLDR;
Perimeter = <u>71.9079 yards</u>
Area = 164.2699 yds^2
Good luck!!
