Mathematics, 20.07.2020 14:01 kksavage36

Find the area and the perimeter of the figure. Use in terms of pi. (no approximations)

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Answer from: rachel63892

See below.

Step-by-step explanation:

So first, we can separate the entire figure into a semi-circle and an isosceles triangle.

AREA:

The area for a semi-circle is $\frac{1}{2}\pi r^2$ .

The diameter is 8cm, so the radius is 4cm.

Area of the semi-circle is:

$\frac{1}{2}(4)^2\pi=\frac{1}{2}(16\pi)=8\pi cm^2$

The area for a triangle is $\frac{1}{2}bh$ .

The base is the same as the diameter (8), and we are given the height as 10. Thus:

$\frac{1}{2} (8)(10)=8(5)=40cm^2$

The total area is $(8\pi +40 )cm^2$

PERIMETER:

The perimeter of a semicircle is: $\pi r + 2r$ (this is derived from dividing the circumference by 2 and then adding on the diameter).

Thus, the perimeter is:

$4\pi +8$

However, we ignore the 8 since the 8 is not part of the perimeter.

The perimeter of the triangle is the two slant lengths. We know the base and the height, so we can use the Pythagorean Theorem:

a^2+b^2=c^2

4^2+10^2=c^2

c^2=116

$c=\sqrt{116}=2\sqrt{29$

Two of them will be $4\sqrt{29}$

Thus, the total perimeter is $4\pi + 4\sqrt{29}$

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

I’m going to infer you said parallel.solve for yy= -1/2x+7/4lines that are parallel have the same slope, different y intercept.so we know m is -1/2then from there solve for y intercept.

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