Geometry WorksheetHeron's Formula & Circle Areas

Name, _Date Period

1. Given a triangle with sides 10, 12, and 14inches long, find the length of the altitude

I upon the 12 inch side. .& -=- \ ~I~\{! / '\ fl.. ---- A: (\<2 ~ ') (11) (<0')\i)/'~ ~Q{7,)(&)('\) io

~v -A=-"6~8 {"G:: ~lf~

A:;~b·~ ;).4~::: \ l\2)~d.4Th c. io -c

4-~ :::.'X

3. Find the area of quadrilateral RSTV ifmLR =90, RS = 12, ST= 8, TV = 7, and VR= 5 .

\2 ~ ~RS\I":::.30

jjJ ~ ~L\1\ 1> ~ '{51 ~ .

y\~ ( 'l~lo)( \)~r;---..!4II-. .;}(J)CJ') tZQ ?>')

I \ -= \~n-=-\L\~+ ~O IJ..-z...

2. Find the area of a parallelogram with twoadjacent sides 8inches and 10 inches long andone diagonal 12 inches long. 30

10 A; ~ z::: 16_---~Io r,l/,.D 7;/J~.

'1.'/// / .l.0 -c •

A~ /~= (?(1)(3)(~)- \SD

4. Given a triangle with sides 4, 6 and 8 incheslong, find the length of the altitude upon theshortest side.

Note: A circle with radius r units has area A = 1t~ and circumference C=2nr or C=nd5. Find the area and circumference of a circle 6. Find the area and circumference of a circle

whose radius is 7. whose diameter is 10.

7. Find the area of the region bounded by two concentric circles withradii 10 inches and 6 inches. 8\3-0- L~-\\'e. 0 .

\oolr - 3 ~ 'Tr:: 64 1\ .-Wv1..

8. The size of a bicycle is determined by the diameter of the wheel. If the bicycle is a 26" bike, andthe wheel turns 10,000 revolutions, how far did the bicycle travel? ..

C~~l\D1\)fO,oOO

9. In order to travel a mile (5280 ft), how many revolutions would the wheel have to make?

~.~ r- \3fl

, ~ 5J,80 ~ X \~21:.__(q ~ 3 tood! I -- ~.J£ ::.175-, 9 to"t: .,

I ~Y".MV= ~ .1lD '\\. ~ \ 15- a 1o.1f

10. A track is formed around a football field by adding a semicircle to each end. How far will anathlete run ifhe makes one lap around the track (running on the inside of the lane)?

360 ft160 ft

12. The following circles are ~gW to each other and to the sides of the rectangle. Find the area ofthe shaded region.·~~ ~- .:'\

R~cA- - ).Gs :: (o(Y2-) ~ d.. ( ~. t) y= 3=- "I d. - \ «S;1\ ~ z.

13. Find the perimeter of the shaded region.2>1o + J. ( (.,'\() -= ~ ~ -}- \ 2 '\r lA

1 .

I' 2..

14. The following four congruent are tangent and a square is created by joining the centers of thecircles. (The side of the square has measure 14.) Find the area of the shaded region.

15. Find the perimeter of the shaded region.

Answers:1. h = 4.J6in.2. A=30,ftin2

3. A = (30 + 14v'3)uZ

4. h= 3f5in5. C = 14.7l"u and A = 491l"uz

6. C = 10Jru and A = 257Z'uz

7. 64Jrinz

8. 260,OOO1t ~ 816,814.1 in9. 775.7revolutions .10. (160.7l"+ 720) "'"1222.7 f+11. 2880 + 6561Z' ~ 4940.9ftz

12. A=(72-18Jr)u2

13. P=(36+127Z')u14. A = (196 - 491Z')uZ

15. P= 14Jru