Math 78 Unit 5: GeometryReview

  1. What is Pi? Why is it important?
  1. How do you find the surface area of a prism?

Proficiency of Skills

  1. What is an isosceles triangle? Draw one with only one 80 degree angle.
  1. What would be:
  • thevertical cross sections through the vertexof a cone, rectangular pyramid and a square pyramid.
  • thehorizontal cross sections of a cone, rectangular pyramid and a square pyramid.
  1. Draw a set of vertical angles (a large “X”). If one angle measures 123 degrees, find the other three!
  1. What is the volume of a
  2. triangular prism with the following dimensions: Height of Prism: 12in, Base of triangle: 13in, Height of TRIANGLE: 9in (Hint: Draw it first).
  3. Cylinder with a diameter of 8ft and a height of 10 feet

Application

  1. A pie has an area of 113.04 in². What is the minimum size of a placemat that can be placed underneath it so that the pie does not touch the table?What is the area of this placemat? Use 3.14 for pi.
  1. A turtle racing track is circular. The diameter of the track is 0.6 miles. If the turtles traveled four times around the track, how many miles did they go?
  1. The top of the Washington Monument is a square pyramid covered with white marble. Each triangular face is 59 feet tall and 35 feet wide. About how many square feet of marble covers the top of the monument if the base is hollow?

For numbers 10 -11, use the following guidelines.

Draw the following figures.

  • If it is possible, is there only one way, more than 1 way?Are the triangles acute, right, or obtuse.
  • If it is possible, draw all possible figures.
  • If it is not possible, then write not possible and explain why.
  1. A triangle with 2 sides measuring 12 cm and 4 cm, and the angle across from the 4 cm side measure 30 degrees.
  1. A triangle with all angles 60 degrees and a side of 8 cm.
  1. In the triangle shown, the measure of is 30 degrees, the measure of is 110 degrees, and the measure of is 50 degrees. What is the measure of?

Label all the angle measures as you find them.

  1. Can a cube have a 5 sided cross section? How about a rectangular pyramid?
  1. Find the area of a right triangle with: base = 15in, height = 5in, hypotenuse = 18.2in
  1. Find the volume AND surface areaof the rectangular prism shown below.

16. Draw seven cubes. Then, find each of the following cross sections from each cube:

square, equilateral triangle, a rectangle that is not a square, a triangle that is not equilateral, a pentagon, a hexagon, an octagon.

Math 78
Unit 2: Geometry
Sample Post Test Answer Key

Problem / Standard / Answer
1. / MCC7.G.4 / Circumference is equal to the diameter times pi
2. / MCC7.G.6 / Find the area of each face and then add them all together; 2(area of base) + 2(area of side) + 2(area of front face)
3. / MCC7.G.2 / 70° angle will be at the top with the bottom two angles each having measures of 55°. The two slanted sides will be the congruent side lengths.
4. / MCC7.G.3 / Vertical = triangle; Horizontal = square/rectangle
5. / MCC7.G.5 / 66° = 180 - 114
6. / MCC7.G.6 / V = ½(16*12)(20) = 1920 units3
7. / MCC7.G.4 / 100 in2
8. / MCC7.G.4 / 5.024 mi
9. / MCC7.G.6 / SA = 5100 ft2
10. / MCC7.G.2 / YES--2 possibilities, one with the leg of 12 and the other with the hypotenuse of 12.
11. / MCC7.G.2 / YES – only one triangle possible; It will be equilateral all sides 6 cm and all angles 60 degrees.
12. / MCC7.G.5 / 49°
13. / MCC7.G.5 / 87°
14. / MCC7.G.5 / 70°
15. / MCC7.G.5 / = 110 degrees. Angles are labeled.

16. / MCC7.G.3 / B
17. / MCC7.G.6 / B
18. / MCC7.G.6 / B
19. / MCC7.G.6 / c
20. / MCC7.G.3 / a. a square

Create 4 points (equidistant from 4 vertexes)—slice.
b. an equilateral triangle

Create 3 points (equidistant from one vertex)—slice
  1. a rectangle that is not a square

Create 4 points (equidistant from 2 vertexes)—slice.
d, a triangle that is not equilateral

Create 3 points (NOT equidistant from a vertex)—slice.
e. a hexagon

Create 6 points on 6 adjacent edges(if the points are the midpoints of the edges, the hexagon will be regular)
f. an octagon
It is not possible to create an octagon (because you can’t get 8 adjacent edges to put points on)
g. a pentagon

Create 5 points on 5 adjacent edges(if the points are the midpoints of the edges, the hexagon will be regular)