Question

1. if a circle has a radius r and an inscribed regular hexagon, what is the perimeter p of the hexagon?

a. p = 6r
b. p = 8r
c. p = 12r
d. p = 6r

1. how do you find the vertices of a regular polygon inscribed in a circle?

a. by calculating the perimeter of the polygon
b. by measuring the angles with a ruler
c. by dividing the circle into equal arcs using the central angles
d. by drawing tangents to the circle

1. which tool is used to create the circle in which a polygon will be inscribed?

a. protractor
b. compass
c. ruler
d. calculator

1. what is the main reason squares are used in urban - planning?

a. they enhance natural beauty
b. they efficiently cover surfaces without gaps
c. they require more material
d. they are difficult to construct

1. what is the mid - point of the line segment connecting (1, 2) and (5, 10)?

a. (-3, -4)
b. (2, 4)
c. (6, 12)
d. (3, 6)

1. what role do right angles play in computer hardware design?

a. reducing energy consumption
b. structuring circuit board layouts
c. increasing processing power
d. enhancing aesthetic appeal

1. how do you calculate the perimeter of a triangle with vertices at (0, 0), (4, 0), and (0, 3)?

a. use the area formula
b. multiply the base by the height
c. use the distance formula for each side and add the results
d. add the integers at all vertices

Explanation:

Step1: Analyze question 1

For a regular hexagon inscribed in a circle of radius r, the perimeter P of a regular hexagon is composed of 6 equal - length sides. Each side has a length equal to the radius r of the circum - circle. So P = 6r.

Step2: Analyze question 2

To find the vertices of a regular polygon inscribed in a circle, we divide the circle into equal arcs using the central angles. For a regular n - gon, the central angle is $\frac{360^{\circ}}{n}$.

Step3: Analyze question 3

A compass is used to create a circle in which a polygon will be inscribed. A compass can draw a circle by keeping a fixed distance (radius) from a central point.

Step4: Analyze question 4

Squares are used in urban planning because they efficiently cover surfaces without gaps. This property is related to the concept of tessellation.

Step5: Analyze question 5

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For points $(1,2)$ and $(5,10)$, the mid - point is $(\frac{1 + 5}{2},\frac{2+10}{2})=(3,6)$.

Step6: Analyze question 6

Right angles play a role in structuring circuit board layouts in computer hardware design. Right - angled shapes are easier to fit together and manage in the layout of components on a circuit board.

Step7: Analyze question 7

To calculate the perimeter of a triangle with vertices $(0,0)$, $(4,0)$ and $(0,3)$, we use the distance formula for each side and add the results. The lengths of the sides are found using $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Answer:

1. d. $P = 6r$
2. c. By dividing the circle into equal arcs using the central angles.
3. b. Compass
4. b. They efficiently cover surfaces without gaps.
5. d. $(3,6)$
6. b. Structuring circuit board layouts
7. c. Use the distance formula for each side and add the results.