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**Section - 1****Ques 1: The radius of a circle is 4. W hat is its area?Ans: **Area of a circle is Ï€r

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Ques 6: The area of a circle is 100Ï€. What is its circumference?

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If the circumference of Circle D is 12Ï€ , the 12Ï€ = 2Ï€r. r = 6. If r = 6, then Area = Ï€(6)

Ques 10: A sector has a central angle of 90Â°. If the sector has a radius of 8, w hat is the area of the sector?

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To find the area of the sector, we need to find the area of the whole circle first. The radius is 8, which means the area is Ï€(8)

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Ques 13: The area of a sector is 1/10th the area of the full circle. What is the central angle of the sector?

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We know the radius is 5, so now we need to find the arc length. Lets begin by determining.

what fraction of the circle the sector is. The central angle of the sector is 72Â°, so the sector is l/5th of the circle, because Now we need to find the circumference. The radius is 5, so the circumference of the circle is 2Ï€(5) = 10Ï€. The arc length of the sector is l/5th the circumference. 1/5 x 10Ï€ = 2Ï€. So now our sector looks like this. The perimeter of the sector is 10 + 2Ï€.

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Ques 16: A triangle has two sides with lengths of 5 and 11, respectively. W hat is the range of values for the length of the third side?

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Alternatively, you can recognize the Pythagorean triplet. This is a 3 -4 -5 triangle.

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**a. 2b .4c. 6d .8Ans: **The lengths of any two sides of a triangle must add up to greater than the length of the third side. The third side must be less than 4 + 8 = 12 and greater than 8 - 4 = 4. So 4 < third side < 12. Only choices c. and d. are in that range.

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Now we can solve for x, because 100 + 60 + x = 180. Solving for x , we get x = 20.

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That means that the length of the third side must be 9.

Ques 23: What is the perimeter of triangle ABC?

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We know the degree measures of two of the angles in Triangle ABC, so we can find the degree measure of the third. Weâ€™ll label the third angle x. We know that 30 + 75 + x = 180. Solving for x we find that x = 75.

Angle BAC and angle BCA are both 75, which means Triangle ABC is an isosceles triangle. If those two angles are equal, we know that their opposite sides are also equal. Side AB has a length of 4, so we know that BC also has a length of 4.

To find the perimeter, we add up the lengths of the three sides. 4 + 4 + 3=11.

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Now we can use the Pythagorean Theorem. (5)

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You should definitely redraw once you discover the triangle is a right triangle!

Now that we know Triangle GHIis a right triangle, we can use the Pythagorean Theorem to find the length of HI. H I is the hypotenuse, so (6)^{2} + (8)^{2} = c^{2}. 36 + 64 = c^{2}. 100 = c^{2}. 10 = c. The length of HI is 10.

Alternatively, we could have recognized the Pythagorean triplet. Triangle GHI is a 6 -8-10 triangle.**Section - 8Ques 26: What is the perimeter of parallelogram ABCD?Ans:** Opposite sides of a parallelogram are equal, so we know that side CD has a length of 7 and side AD has a length of 8. So the perimeter is 7 + 8 + 7 + 8 = 30.

Alternatively, the perimeter is 2 x (7 + 8) = 30. We can say this because we know that 2 sides have a length of 7 and 2 sides have a length of 8.

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So we know that 7 + x + 7 + x = 18 â†’ 2x + 14 = 18 â†’ 2x = 4 â†’ x = 2

The length of side EH is 2.

Ques 29: What is the area of Rectangle ABCD?

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Now we can use the Pythagorean Theorem to find the length of diagonal AC, which is the hypotenuse of right triangle ABC. We can also recognize that this is a Pythagorean Triplet â€” a 5 - 12 - 13 triangle. The length of diagonal AC is 13.

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8 x 6 = 48.

That means that the area of Rectangle EFGH is also 48. We can use the area and the length of side EF to solve for the length of side FG. 12 x (FG) = 48. The length of side FG is 4.

Ques 32: What is the perimeter of a square with an area of 25?

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The square has four equal sides, so that means that the perimeter is 4 times the length of one side. If we designate the length of the sides of the square s, then the perimeter is 4

That means that the area of the rectangle is also 64. We know the length of the rectangle is 4, so we can solve for the width. 4 x (width) = 64. The width is 16.

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Ques 35: Draw a coordinate plane and plot the following points:

1 .(2 ,3 )

2. (- 2 ,- 1 )

3. (- 5 ,- 6 )

4. (4 ,-2 .5 )

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Ques 38: Does the point (-3 ,0 ) lie on the curve y = x

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y = (-3)

y = 9 - 3 = 6

y does not equal 0 when x equals - 3, so the point does not lie on the curve.

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7 = 12 + 2 = 14

The y-coordinate is 14. The point is (3, 14).

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