Explanation:

One mile is equal to 5,280 feet; one fourth of a mile is equal to

Each of the six congruent sides measures one sixth of this, or

Teresa runs clockwise from Point A to halfway between Point E and Point F, so she runs along four and one half sides, for a total of

Explanation:

Explanation:

The sum of the interior angles of a polygon is given bywhere= number of sides of the polygon. An octagon has 8 sides, so the formula becomes

Explanation:

To solve, simply use the formula to find the total degrees inside a polygon, where n is the number of vertices.

In this particular case, a hexagon means a shape with six sides and thus six vertices.

Thus,

Explanation:

Because it can be split into twotriangles, the area of an equilateral triangle can be expressed as...

With that in mind, the equilateral triangle in question has area of.

Now consider that a regular hexagon can be split into six congruent equilateral triangles with a vertex at the center and the side opposite the center as one of the hexagon's sides (a handy way of finding a hexagon's area if you can't use the regular polygon formula requiring an apothem.) Knowing that, our answer is.

Explanation:

How do you find the area of a hexagon?

有几种方法可以找到hexag的面积on.

1. In a regular hexagon, split the figure into triangles.
2. Find the area of one triangle.
3. Multiply this value by six.

Alternatively, the area can be found by calculating one-half of the side length times the apothem.

Regular hexagons:

Regular hexagons are interesting polygons. Hexagons are six sided figures and possess the following shape:

In a regular hexagon, all sides equal the same length and all interior angles have the same measure; therefore, we can write the following expression.

One of the easiest methods that can be used to find the area of a polygon is to split the figure into triangles. Let's start by splitting the hexagon into six triangles.

In this figure, the center point,, is equidistant from all of the vertices. As a result, the six dotted lines within the hexagon are the same length. Likewise, all of the triangles within the hexagon are congruent by the side-side-side rule: each of the triangle's share two sides inside the hexagon as well as a base side that makes up the perimeter of the hexagon. In a similar fashion, each of the triangles have the same angles. There arein a circle and the hexagon in our image has separated it into six equal parts; therefore, we can write the following:

We also know the following:

Now, let's look at each of the triangles in the hexagon. We know that each triangle has two two sides that are equal; therefore, each of the base angles of each triangle must be the same. We know that a triangle hasand we can solve for the two base angles of each triangle using this information.

Each angle in the triangle equals. We now know that all the triangles are congruent and equilateral: each triangle has three equal side lengths and three equal angles. Now, we can use this vital information to solve for the hexagon's area. If we find the area of one of the triangles, then we can multiply it by six in order to calculate the area of the entire figure. Let's start by analyzing. If we draw, an altitude through the triangle, then we find that we create twotriangles.

Let's solve for the length of this triangle. Remember that intriangles, triangles possess side lengths in the following ratio:

Now, we can analyzeusing the a substitute variable for side length,.

We know the measure of both the base and height ofand we can solve for its area.

Now, we need to multiply this by six in order to find the area of the entire hexagon.

We have solved for the area of a regular hexagon with side length,. If we know the side length of a regular hexagon, then we can solve for the area.

如果我们不是普通的六边形,然后我们一个solve for the area of the hexagon by using the side length(i.e.) and apothem (i.e.), which is the length of a line drawn from the center of the polygon to the right angle of any side. This is denoted by the variablein the following figure:

Alternative method:

If we are given the variablesand, then we can solve for the area of the hexagon through the following formula:

In this equation,is the area,is the perimeter, and是边心距。我们必须计算周长ing the side length and the equation, whereis the side length.

解决方案:

In the given problem we know that the side length of a regular hexagon is the following:

Let's substitute this value into the area formula for a regular hexagon and solve.

Simplify.

Round the answer to the nearest whole number.

Explanation:

We know that the sum of all the angles must be 180 and we already know one angle is 90, leaving the sum of x and y to be 90.

Solve for x to find y.

One third of 21 is 7. Four less than 7 is 3. So if angle x is 3 then that leaves 87 for angle y.

Explanation:

The first thing to notice is that this is a 30^o:60^o:90^otriangle. If you draw a diagram, it is easier to see that the angle that is asked for corresponds to the side with a length of 4. This will be the smallest angle. The correct answer is 30.

Explanation:

In the figure above, angleADBis a right angle. Because sideACis a straight line, angleCDBmust also be a right angle.

Let’s examine triangleADB. The sum of the measures of the three angles must be 180 degrees, and we know that angleADBmust be 90 degrees, since it is a right angle. We can now set up the following equation.

x+y+ 90 = 180

Subtract 90 from both sides.

x+y= 90

Next, we will look at triangleCDB. We know that angleCDBis also 90 degrees, so we will write the following equation:

y– 10 + 2x– 20 + 90 = 180

y+ 2x+ 60 = 180

Subtract 60 from both sides.

y+ 2x= 120

We have a system of equations consisting ofx+y= 90 andy+ 2x= 120. We can solve this system by solving one equation in terms ofxand then substituting this value into the second equation. Let’s solve foryin the equationx+y= 90.

x+y= 90

Subtractxfrom both sides.

y= 90 –x

Next, we can substitute 90 –xinto the equationy+ 2x= 120.

(90 –x) + 2x= 120

90 +x= 120

x= 120 – 90 = 30

x= 30

Sincey= 90 –x,y= 90 – 30 = 60.

The question ultimately asks us to find the positive difference between the measures ofACBandCBD. The measure ofACB= 2x– 20 = 2(30) – 20 = 40 degrees. The measure ofCBD=y– 10 = 60 – 10 = 50 degrees. The positive difference between 50 degrees and 40 degrees is 10.

The answer is 10.

Explanation:

In any given triangle, the sum of any two sides is greater than the third. The incorrect answers have the sum of two sides equal to the third.