1. 37 degree. A triangle has 180 there is a right angle 90 and then c is 53 which leaves 37 for a
Answer:
12
Step-by-step explanation:
12 +30= 42
42+12=54
Answer:
Part 1) ![A=36(\pi-2)\ cm^2](https://tex.z-dn.net/?f=A%3D36%28%5Cpi-2%29%5C%20cm%5E2)
Part 2) ![P=6(\pi+2\sqrt{2})\ cm](https://tex.z-dn.net/?f=P%3D6%28%5Cpi%2B2%5Csqrt%7B2%7D%29%5C%20cm)
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
Part 1) Find the area
we know that
The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle
so
![A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%5Cpi%20r%5E%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%28b%29%28h%29)
we have that the base and the height of triangle is equal to the radius of the circle
![r=12\ cm\\b=12\ cm\\h=12\ cm](https://tex.z-dn.net/?f=r%3D12%5C%20cm%5C%5Cb%3D12%5C%20cm%5C%5Ch%3D12%5C%20cm)
substitute
![A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)\\A=(36\pi-72)\ cm^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%5Cpi%20%2812%29%5E%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%2812%29%2812%29%5C%5CA%3D%2836%5Cpi-72%29%5C%20cm%5E2)
simplify
Factor 36
![A=36(\pi-2)\ cm^2](https://tex.z-dn.net/?f=A%3D36%28%5Cpi-2%29%5C%20cm%5E2)
Part 2) Find the perimeter
The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle
The circumference of a quarter of circle is equal to
![C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B1%7D%7B4%7D%282%5Cpi%20r%29%3D%5Cfrac%7B1%7D%7B2%7D%5Cpi%20r)
substitute the given values
![C=\frac{1}{2}\pi (12)\\C=6\pi\ cm](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B1%7D%7B2%7D%5Cpi%20%2812%29%5C%5CC%3D6%5Cpi%5C%20cm)
Applying the Pythagorean Theorem
The hypotenuse of right triangle is equal to
![AC=\sqrt{12^2+12^2}\\AC=\sqrt{288}\ cm](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B12%5E2%2B12%5E2%7D%5C%5CAC%3D%5Csqrt%7B288%7D%5C%20cm)
simplify
![AC=12\sqrt{2}\ cm](https://tex.z-dn.net/?f=AC%3D12%5Csqrt%7B2%7D%5C%20cm)
Find the perimeter
![P=(6\pi+12\sqrt{2})\ cm](https://tex.z-dn.net/?f=P%3D%286%5Cpi%2B12%5Csqrt%7B2%7D%29%5C%20cm)
simplify
Factor 6
![P=6(\pi+2\sqrt{2})\ cm](https://tex.z-dn.net/?f=P%3D6%28%5Cpi%2B2%5Csqrt%7B2%7D%29%5C%20cm)
Answer:
16+c
Step-by-step explanation:
Sum means we will have to add. When it says "sum of sixteen and c" it is telling us to add both sixteen and c together.