For #1, the area of a trapezoid will be found with the formula 1/2(b1+b2)h
1/2(7+17)5
1/2*24*5
12*5=60
So the first one is 60cm^2
For #2, we first need to find total angle measure in the shape. This is found be doing:
180(n-2), where n is the number of the sides
180(10-2)
180*8=1440
Then we need to find how much each angle is. We do this by dividing the angle measure by the number of sides.
1440/10=144
You might say that we've reached the conclusion, but we haven't. We found the obtuse angle measure (twice the angle measure of angle 2), so we'll divide by two to get that angle 2 = 72.
Since the shape is composed of isosceles triangles, we can say that the opposite angle is also equal to 72. We can therefore write:
72+72+x=180
144+x=180
x=36
So angle 2 is equal to 36 degrees.
For #3, all we have to keep in mind are these ratios:
Perimeter: s1/s2, where s1 and s2 correspond to your side lengths
Area: (s1)^2/(s2)^2, where s1 and s2 still are side lengths, but you now square them
30/12 = 5/2
30^2+12^2 = 900/144 = 25/4
So the first choice is your answer
For the pentagon, we'll use a slightly complicated formula:
[tex] \frac{1}{4} \sqrt{5(5+2 \sqrt{5})x^2 } [/tex]
Where x is the side length. This gets us approximately 172.0 cm^2
For the last problem, a minor arc is an arc that is less than 180. We see that arc AB, which measures 115. So the answer is the second choice.
