# Category Archives: geometry problems of the day

## #19 Regular Hexagon

19. If a regular hexagon has sides equal to 12, what is the area? (this problem comes up over and over again in different ways. make sure you can work it!)

Answer: 62.4 sq. units. You can find this using the formula for the area of a regular polygon, (1/2 x apothem x perimeter). You can also find the area of one equilateral triangle with side 12, and multiplying that by 6.20. Given a pentagonal prism.
a. How many total vertices? 10
b. How many lateral faces? 5
c. How many total faces? 7
d. How many bases? 2

F+V=e+2 Total Faces + Vertices = edges + 2

21. Find the area of an equilateral triangle with perimeter 18.
If perimeter is 18, then each side is 6. Area: 15.6 sq. units

22. If a circle has diameter 20, find: (so radius is 10)
a. area of the circle 100 pi or 314.2 sq. units
b. circumference of the circle 62.8
c. volume of a sphere with the same diameter 4188.8 cu. un.
d. area of a sphere with the same diameter 1256.5 sq.un.
e. area of semi-circle 50 pi sq. un. or 157.1 sq. un.

## Prob #18 Similar Polygons

Given 2 similar triangles. The ratio of their sides is 2:3.

a. What is the ratio of the perimeters of the triangles? 2:3

b. What is the ratio of the altitudes of the triangles? 2:3

c. What is the ratio of the medians of the triangles? 2:3

d. What is the ratio of the angle bisectors of the triangles? 2:3

e. What is the ratio of the areas of the triangles? 4:9

f. What is the scale factor of the triangles? 2:3

Answer: ALL corresponding linear parts are in the same ratio as the sides. The ratio of the areas is the ratio of the sides squared. The ratio of the volumes is the ratio of the sides cubed.

## #14-What Is A Central Angle? ## Geometry Practice Problems for Thursday

Good Morning! Today is the last school day before Spring Break for some people. Woo hoo! Enjoy!

Today’s problems are very basic and are just to help you remember the basics. All answers for this week will be posted on Saturday. If you would like personal feedback, email me at realmathinaminute@hotmail.com.

9. The perimeter of a square is 68 meters. If one side is 3x+2, what is the value of x?

10. A right triangle has legs of 24 inches and 18 inches. Find the length of the hypotenuse.
Answer: The hypotenuse = 30. The answer is found using the Pythagorian Thm. It is in the 3-4-5 family.

11. Two angles are supplementary. One is 68 degrees. Find the other angle.
Answer: 112 degrees. Supplementary angles are two angles that add up to 180.

12. If the radius of a circle is 5, find the:

Area: 25 pi sq. units or 78.54 sq. units

Circumference: 10 pi units or 31.4 units

(on a multiple choice test answers may be left in terms of pi or may be written as a decimal. Be able to recognize the answer in either form.

Have a great break….or just a great weekend. See you Monday!

## Geometry EOCT Problems 5-8

Welcome back! Send me you answers! If you have not started these problems yet, go back to #1 on yesterday’s post and get started. Keep a notebook with all of your problems worked out.

5. If a=b and b=c, than a=c illustrates which property?
a. Reflexive b. Commutative c. Transitive d. Distributive

6. Given A = (6,3) and B = (8, -2). Find AB. (AB means the distance from A to B).
The formula you need for this problem is on the formula sheet. Just make sure you know how and when to use it.

7. Given: “If a, then b.” Write the:
Inverse: “If not a, then not b.” Could be written: “If ~a, then ~b.”

Contrapositive: “If not b, then not a.” Could be written: “If~b, then ~a.”

8. Draw a triangle that has two angles which each measure 43 degrees.
a. Is the triangle isosceles, equilateral, or scalene?
b. What is the measure of the 3rd angle?
c. Is the triangle right, acute, or obtuse?

Answer: The triangle is isosceles because 2 sides are congruent. The 3rd angle measures 94 degrees, so the triangle is obtuse.

Enjoy the rest of the day! See you tomorrow!

The Mathster
realmathinaminute@hotmail.com

## Geometry EOCT Problems 1-4

First Day!!!

Good idea to keep all of these problems worked in a notebook. That way you can review it all right before the test…and you can share it with your teacher.

This set of problems is to help you “remember” way back to beginning of the year.

1. What is the “converse” of the following statement? What is the hypothesis? What is the conclusion?

If Jenny goes to the ballgame, then she will wear her red jacket.

a. Converse: If Jenny wears her red jacket, then she will go to the ballgame.
b. Hypothesis: If Jenny goes to the ballgame
c. Conclusion: Then she will wear her red jacket.

2. Which word describes a triangle whose angles measure 23, 38, and 119 degrees?
a. isosceles b. acute c. right d. obtuse
d. Obtuse

3. Find the midpoint of a segment with endpoints (3, 7) and (5, -1).
Midpoint is (4 , 3)

4. What is the area of a circle with radius = 4 cm? Leave pi in your answer.
Area is 16 pi sq. cm. or 50.27 sq. cm.

Email your answers to realmathinaminute@hotmail.com. Put EOCT as the subject. If you want me to communicate with your teacher, send me that information too.

Congratulations for getting started! Come back tomorrow.