9514 1404 393
Answer:
88 square inches
Step-by-step explanation:
The figure can be divided into two congruent trapezoids, each with bases 7 and 4 inches, and height 8 inches. Then the total area is ...
A = 2(1/2)(b1 +b2)h
A = (7 +4)(8) = 88 . . . . square inches
The angle in a regular polygon is ((n-2)*180)/n with n being the number of sides. The exterior angles would be (360)/n since exterior angles add up to 360. Therefore, (360)/n= (((n-2)*180)/n)*1/3. Multiplying both sides by n, we get 360=((n-2)*180)*1/3. After that, we divide both sides by 180 and multiply both sides by 3 to get 6=n-2. Therefore, n=8 and it is an octagon
8^2+6^2=c^2. 64+36=c^2. c=10. Here we use Pythagorean theorem which is a^2+b^2=c^2.
Answer:
Puppy Liz runs 34.61 ft.
Step-by-step explanation:
From the figure we can extract two triangles: one with angle 34° and adjacent 40ft, the other with angle 34°+23° and adjacent 40ft.
Let us call the distance from the pole to the fire hydrant
, and the distance from the pole to the bench
, then the distance
from the fire hydrant to the bench is
![d=d_2-d_1](https://tex.z-dn.net/?f=d%3Dd_2-d_1)
which is the distance the Puppy Liz runs.
Now, from trigonometry we have
![tan(34^o)=\frac{d_1}{40}\\\\\therefore d_1= 40*tan(34^o)\\\\ \boxed{d_1=26.98ft}](https://tex.z-dn.net/?f=tan%2834%5Eo%29%3D%5Cfrac%7Bd_1%7D%7B40%7D%5C%5C%5C%5C%5Ctherefore%20d_1%3D%2040%2Atan%2834%5Eo%29%5C%5C%5C%5C%20%5Cboxed%7Bd_1%3D26.98ft%7D)
and
![tan(34^o+23^o)=\frac{d_2}{40}](https://tex.z-dn.net/?f=tan%2834%5Eo%2B23%5Eo%29%3D%5Cfrac%7Bd_2%7D%7B40%7D)
![d_2=40*tan(34^o+23^o)\\\\\boxed{d_2=61.59}](https://tex.z-dn.net/?f=d_2%3D40%2Atan%2834%5Eo%2B23%5Eo%29%5C%5C%5C%5C%5Cboxed%7Bd_2%3D61.59%7D)
Therefore, the distance
Puppy Liz runs is
![d=d_2-d_1](https://tex.z-dn.net/?f=d%3Dd_2-d_1)
![d=61.59ft-26.98ft\\\\\boxed{d=34.61ft}](https://tex.z-dn.net/?f=d%3D61.59ft-26.98ft%5C%5C%5C%5C%5Cboxed%7Bd%3D34.61ft%7D)
Answer:
AAS Congruence Theorem
Step-by-step explanation:
I see 2 angles of one triangle shown to be congruent to 2 angles of the other triangle. After the two angles, there is a side in common to both triangles which is congruent to itself. That makes angle-angle-side.
Answer: AAS Congruent Theorem