1)you can use any side as the__ of a triangle.2)An ___ is a region blinded by an arc and the two radii to the arcs endpoints.3)the distance from the center to a vertex is the ___ of a regular polygon.4)two arcs of a circle with exactly one point in common are ___. 9) A triangle has legs measuring 5ft and 12ft, and hypotenuse measuring 13ft. What is the area? 13) is the picture above. 17) what is the area of a regular hexagon with a perimeter of 240cm?I have more questions but will post separately because they are all pictures!!!!

Accepted Solution

(1) Base
(2) Sector of a circle
(3) Radius
(4) Adjacent arcs
(9) 30
(13) 256 ft^2
(17) 4156.92 cm^2

(1) It's a common convention that you can choose any side of a triangle as a base, but in specific cases like in the right-angled triangle, the base should always be the adjacent leg with which the 90 degree angle is made. In other words, in the case of right-angled triangle, the two legs of a triangle must be perpendicular to one another (meaning make 90 degrees angle). But in general triangles you can choose any side as a base of a triangle.

(2) The image is attached below. As you can see that a sector of a circle is actually the region which is shaded. Two radii that meet at the end points of an arc yield a region within a circle know as "sector". Hence the correct fill in the blank is the "sector of a circle." 

(3) The radius of a regular polygon is the distance from the center to any vertex. It is the same for each and every vertex. The radius is also the radius of the polygon's circumcircle, which is the circle that passes through every vertex. In this role, it is sometimes called the circumradius. Hence the correct answer is "radius."

(4) Adjacent arcs in simple words are the arc that lie next to each other. They have one point in common being next to each other. Hence the correct answer is adjacent arcs. One interesting fact is that a circle is made up of very large number of adjacent arcs.

(9) As the hypotenuse is mentioned, it means that it is a right-angled triangle; therefore:

Area of a right angled triangle = 1/2 * base * height
Area of a right angled triangle = 1/2 * 5* 12 = 30 ft^2

(13) The picture consists of FOUR right-angled triangles (making a parallelogram) therefore the area would be:
Area = 4 * 1/2 * base * height
Area = 4 * 1/2 * 12.8* 10 = 256 ft^2

(17) The general formula for the area of a polygon is:
Area = [tex] \frac{3 \sqrt{3} a^2 }{2} [/tex]

Where P = perimeter = 6a (hexagon)
=> a = P/6 

Plug in the values
Area = [tex]\frac{ \sqrt{3} P^2 }{24} = \frac{ \sqrt{3} (240)^2 }{24} = 4156.92 cm^2[/tex]