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Eleventh Grade (Grade 11) Two Dimensional Shapes Questions

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Grade 11 Triangles
In ΔABC, AB=5.2 units, AC=4.4 units, and BC=2.5 units. What is the area of the triangle?
Obtuse Triangle ABC v3
  1. 5.5 units2
  2. 31.7 units2
  3. 50.2 units2
  4. 78.6 units2
Grade 11 Triangles
In ΔABC, AB=5.4 units, BC=14.3 units, and AC=16.2 units. What is the area of the triangle, rounded to one decimal place?
Acute Triangle ABC v2
  1. 9.0 units2
  2. 35.1 units2
  3. 37.9 units2
  4. 51.7 units2
Grade 11 Quadrilaterals
A square whose area is 144 sq. in. has an apothem of                           .
  1. 6 inches
  2. 6√2 inches
  3. 6√3 inches
  4. none of these
Grade 11 Circles
Write an equation for the circle with center (2,1) that passes through (2,4).
  1. (x-2)2+(y-1)2=9
  2. (x-2)2+(y-1)2=3
  3. (x+3)2+(y+1)2=9
  4. (x+3)2+(y+1)2=3
Grade 11 Circles CCSS: HSG-GPE.A.1
What is the center and radius of the circle given by the following equation?
x2+y2-18x+6y+65=0
  1. Center:(18,-6), Radius:65
  2. Center:(9,-3), Radius:5
  3. Center:(0,0), Radius:√65
  4. Center:(-9,3), Radius:25
Grade 11 Circles CCSS: HSG-GMD.A.1

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

Rearranging the equation from the previous step, we find that C=2πr, which is the formula for the circumference of a circle. If we had started with a circle such that d≠1, would we have been able to derive the correct formula? Why or why not?
  1. No, a circle with a larger or smaller diameter would have had a larger or smaller circumference, and so the value found in step H would have been different.
  2. No, a circle with d≠1 would also have r≠12, and so the formula would be different.
  3. Yes, because other calculations would be performed to compensate for this, and thus arrive at the correct formula.
  4. Yes, since the ratio of a circle's diameter to its circumference is always the same, it doesn't matter what the length of the original circle's diameter is.
Grade 11 Circles CCSS: HSG-GPE.A.1
What is the center and radius of the circle given by the following equation?
x2+y2-2x+10y+22=0
  1. Center:(0,0), radius:√22
  2. Center:(-2,10), radius:√22
  3. Center:(1,-5), radius:2
  4. Center:(1,-5), radius:4
Grade 11 Circles CCSS: HSG-GMD.A.1

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

Thus far, only a circle of radius 1/2 was used. Which of the following formulas would correctly relate this circle with a new circle of unknown circumference, C, and radius, r. Why?
  1. Cπ=r12 because all circles are similar.
  2. C=12rπ since the new circle will depend on the measurements of the circle already investigated.
  3. C2=πr2 because the area of a circle is related to its circumference.
  4. C=nπ,r=n2 since the new circle's circumference and radius will depend upon the number of sides of an inscribed regular polygon.
Grade 11 Circles CCSS: HSG-GMD.A.1

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

Using the formula in part C, find the perimeter of an inscribed regular 20-sided polygon in circle A.
  1. 0.1564
  2. 3.1287
  3. 6.2574
  4. 0.3129
Grade 11 Circles CCSS: HSG-GMD.A.1

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

Using the formula in part C, find the perimeter of an inscribed regular 200-sided polygon in circle A.
  1. 62.5738
  2. 6.2829
  3. 0.0157
  4. 3.1415
Grade 11 Circles CCSS: HSG-GMD.A.1

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

Using the formula from the previous question, find the perimeter of an inscribed regular hexagon in circle A.
  1. 3
  2. 1/2
  3. 6
  4. 12
Grade 11 Circles CCSS: HSG-GMD.A.1

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

Using the formula in part C, find the perimeter of an inscribed regular 100-sided polygon in circle A.
  1. 30.9017
  2. 6.2822
  3. 0.0314
  4. 3.1411
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