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Eleventh Grade (Grade 11) Two Dimensional Shapes Questions

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Grade 11 Triangles
Triangles that have the exact same shape but different area are called                      .
  1. Similar Triangles
  2. Regular Polygons
  3. Tangents
  4. Equilateral Triangles
  5. Isosceles Triangles
Grade 11 Triangles
If a triangle has no equal sides and no equal angles then it is
  1. right.
  2. scalene.
  3. obtuse.
  4. isosceles.
Grade 11 Triangles
If a triangle has no equal sides and one right angle, then it is which of the following types of triangles?
  1. Scalene Acute
  2. Isosceles Right
  3. Scalene Right
  4. None of the above
Grade 11 Triangles
The sides of [math]Delta ABC[/math] form the ratio [math]9:10:11[/math]. If the perimeter of the triangle is [math]15 \ "units"[/math], what is the area of the triangle?
Equilateral Triangle ABC v1
  1. [math]3.9 \ "units"^2[/math]
  2. [math]10.6 \ "units"^2[/math]
  3. [math]42.4 \ "units"^2[/math]
  4. [math]122.3 \ "units"^2[/math]
Grade 11 Circles
If the points (1, 2) and (-5, 2) are endpoints of a diameter of a given circle, what is the equation of this circle?
  1. [math] (x-1)^2 + (y-2)^2 = 1 [/math]
  2. [math] (x+5)^2 + (y-2)^2 = 9 [/math]
  3. [math] (x+2)^2 + (y-2)^2 = 9 [/math]
  4. [math] (x+3)^2 + y(-1)^2 = 3 [/math]
Grade 11 Two Dimensional Shapes
A polygon that is always convex.
  1. Triangle
  2. Quadrilateral
  3. Circle
  4. N-gon
  5. None of the above
Grade 11 Circles
Given the equation of a circle, [math](x-3)^2+(y+5)^2=10[/math], what is the circle's radius?
  1. [math]5[/math]
  2. [math]100[/math]
  3. [math]sqrt5[/math]
  4. [math]sqrt10[/math]
Grade 11 Circles CCSS: HSG-GMD.A.1

This question is a part of a group with common instructions. View group »

As the number of sides continues to increase, will the value of the perimeter continue to increase without bound? Or is it approaching some value? Why?
  1. The perimeter value will continue to increase without bound, because the number of sides will keep increasing.
  2. The perimeter value will continue to increase without bound, because n is increasing at a faster rate than a is decreasing.
  3. The perimeter value will approach a certain value, since it is bounded by the circumference of the circle. The value seems to be [math]pi[/math].
  4. The perimeter value will approach a certain value, because as n increases, a decreases. The value seems to be 4.
Grade 11 Triangles
In [math]Delta ABC[/math] , [math]AB = 1.3 \ "units"[/math], [math]BC = 1.7 \ "units"[/math], and [math]AC = 1.9 \ "units"[/math]. What is the area of the triangle rounded to one decimal place?
Isosceles Triangle ABC v2
  1. [math]0.2 \ "units"^2[/math]
  2. [math]0.7 \ "units"^2[/math]
  3. [math]0.9 \ "units"^2[/math]
  4. [math]1.1 \ "units"^2[/math]
Grade 11 Circles
Write an equation for a circle if the endpoints of a diameter are at (1,1) and (1,-9).
  1. [math](x-1)^2+(y+4)^2=5[/math]
  2. [math](x-1)^2+(y+4)^2=25[/math]
  3. [math](x+1)^2+(y-4)^2=5[/math]
  4. [math](x+1)^2+(y-4)^2=25[/math]
Grade 11 Circles CCSS: HSG-GMD.A.1

This question is a part of a group with common instructions. View group »

Let triangle ABC be one of the triangles of the inscribed polygon referred to in the previous questions. Here, A would be the center of the circle, B and C would lie on the circle, and [math]bar{BA}[/math] and [math]bar{AC}[/math] have lengths determined in the previous question. To determine the length of [math]bar{BC}[/math], which will be called [math]a[/math], one can use the formula [math]a=2r sin((360°)/(2n))[/math], where r is the radius of the circle and n is the number of sides of the inscribed polygon. Which of the following gives the best reasoning for why the argument of the sine function, which is half of [math]m ang BAC[/math], is [math](360°)/(2n) ?[/math]
Equilateral Triangle Height v2
  1. Since a triangle has 180°, to divide by 2n you must multiply the numerator by 2 as well.
  2. To account for the conversion from radians to degrees, 1/n is multiplied by 360°/2.
  3. It depends on the size of the circle, but in this case, where r = 1/2, 360°/n is multiplied by 1/2.
  4. The inscribed polygon is divided into n triangles, and then half of that would mean dividing a full rotation by 2n.
Grade 11 Quadrilaterals
A square whose area is 144 sq. in. has an apothem of                           .
  1. 6 inches
  2. [math]6sqrt2[/math] inches
  3. [math]6sqrt3[/math] inches
  4. none of these
Grade 11 Circles
Write an equation for the circle with center (2,1) that passes through (2,4).
  1. [math](x-2)^2+(y-1)^2=9[/math]
  2. [math](x-2)^2+(y-1)^2=3[/math]
  3. [math](x+3)^2+(y+1)^2=9[/math]
  4. [math](x+3)^2+(y+1)^2=3[/math]
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