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3 years ago

Which polygons are congruent?

1 answer:

4 0

Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal. Move your mouse cursor over the parts of each figure on the left to see the corresponding parts of the congruent figure on the right.

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Compare the perimeters of the two regular figures. Which statement is true?

adell [148]

Answer:

(A). The perimeter of the octagon is greater than that of the hexagon.

Step-by-step explanation:

Since, hexagon consists of 6 sides and 6 angles, thus the measure of one angle of the hexagon will be= $\frac{(n-2){\timeS}180^{\circ}}{6}$

= $\frac{(6-2){\timeS}180^{\circ}}{6}$

= $\frac{(4){\timeS}180^{\circ}}{6}$

= $120^{\circ}$

Now, since MQ is the angle bisector of the one of the angle of the hexagon, therefore ∠QMP=60°.

Now, from ΔQMP. we have

$\frac{MP}{MQ}=cos60^{\circ}$

$MP=\frac{1}{2}$

Thus, the perimeter of the hexagon is:

$P=12{\times}MP$

$P=12{\times}\frac{1}{2}$

$P=6 units$

Thus, the perimeter of hexagon is 6 units.

Also, Since, octagon consists of 8 sides and 8 angles, thus the measure of one angle of the octagon will be= $\frac{(n-2){\timeS}180^{\circ}}{8}$

= $\frac{(8-2){\timeS}180^{\circ}}{8}$

= $\frac{(6){\timeS}180^{\circ}}{8}$

= $135^{\circ}$

Now, since AP is the angle bisector of the one of the angle of the octagon, therefore ${\angle}PAC=cos\frac{135}{2}$ .

From ΔAPC, we have

$AC=cos\frac{135}{2}$

Now, Perimeter of octagon is:

$P=16{\times}cos\frac{135}{2}$

$P=16{\times}0.382$

$P=6.122 units$

Thus, the perimeter of octagon is 6.122 units.

Now, the perimeter of octagon is greater than perimeter of the hexagon, thus option A is correct that is The perimeter of the octagon is greater than that of the hexagon.

4 0

3 years ago

What is the answer and formula for 7f+5=68

gladu [14]

7f=68-5
7f=63
f=63/7
f=9

4 0

3 years ago

Find the Point-Slope equation of the line that passes through the given points. (0,8), (-1,10)

patriot [66]

The slope of the equation is -2

8 0

3 years ago

Read 2 more answers

If a gardner plants beans in 1/8 of a plot and tomatoes in 1/6 of a plot, what fraction of the garden is left for other crops

JulsSmile [24]

You simply have to sum the two fraction together to get the total amount of occupied plot. To do so, multiply both numerator and denominator of each fration by the same number, so that they end up having the same denominator.

You can multiply both numerator and denominator of 1/8 by 3 to get 3/24. Similarly, you can multiply both numerator and denominator of 1/6 by 4 to get 4/24.

Now we can easily sum the two fractions together:

$\dfrac{1}{8}+\dfrac{1}{6}=\dfrac{3}{24}+\dfrac{4}{24} = \dfrac{7}{24}$

So, if 7 parts out of 24 are occupied, it means that there are $24-7=17$ parts left for other crops. So, the answer is 17/24.

5 0

3 years ago

Solve the equation. -4 (y - 2) = 12 y = ?

inna [77]

First you distribute what’s outside the parentheses (the -4)

-4•4= -4y
-4•-2= 8

New equation: -4y+8=12

Now you solve like a normal equation
12-8 is 4

New equation: -4y=4

Now divide

Answer:-1

8 0

3 years ago