zName: _______________________ Unit 10 Review

Geometry Pd. ___ Date: _____

Big Ideas of Unit 10!

This packet must be completed in its entirety by the start of class tomorrow!

10-1 Unit conversion

KHDUDCM - - -Metrics! Set up proportions using the reference sheet for the imperial system!

10-2 Area of basic polygons and Trigonometry

Use basic formulas as well as trig ratios (SOHCAHTOA) and Pythagorean Theorem to help you solve for missing parts of area formulas (height or base of triangles)

10-3 Area of a Regular Polygon

Need to “break up the figure” into triangles

Steps:1. Calculate the central angle (360/n)2. If not already there, draw in the altitude

(mark the right angles) and bisect the central angleto find the vertex angle of the small RIGHT triangle.

3. Bisect the base of the isosceles triangle to find the length of one side of the right triangle.

4. Use trig to calculate the length of the height5. Find the area of 1 triangle6. Multiply the area by the # of triangles in the regular

polygon.10-4 Area of COMPOSITE Regions

If the problem is asking for a big area of more than one shape:Find the area of each and add

10-5 Area of Slanted Polygons

Remember! Box method! Each polygon should have two sides that are ⊥.

If the problem is asking for the area of a shaded region: TACO

“Total area minus cut out”

Station 1: Conversions and Areas of Geometric ShapesComplete the following conversions in the table below:

4.033 km = ___ m 999.5 mg = ___ hg

6 miles = ___ yd 57 in = ___ mm

For questions 1 and 2 use the following diagram of triangle ABC with altitude CD drawn

1. Determine the area of triangle ABC

2. Determine the area of triangle BCD

3. Given the following trapezoid, determine and state the area.

4. Determine the area of a circle whose diameter is 20 inches. Leave your answer in terms of pi.

5. Determine the area of a semi-circle whose radius is 3.2 feet. Round your answer to the nearest tenth of a foot.

6. Determine the area of the following parallelogram:

7. Determine the area of the triangle to the nearest tenth.

8. Determine the area of the triangle to the nearest tenth. – (*Remember, you need base AND height)!

9. Determine the area of the rectangle to the nearest whole.

Station 2: Area of a Regular Polygon

10. Calculate the area of the regular hexagon below. Round your answer to the nearest 10th.

11.Find the area of the regular octagon to the nearest 10th.

Station 3: Area of COMPOSITE Regions

12. In the accompanying diagram, right triangle ABC is inscribed in a circle. BA is the diameter, BC =6 cm, AC = 8 cm. Find the exact area of the shaded region. Leave your answer in terms of π

13. The figure shown is composed of 2 semicircles. BC = 2 and AD = 6. Find the area of the shaded region in terms of Pi.

14. The diagram below shows two equilateral triangles. If AD = 6 and BC = 2, find the area of the composite figure to the nearest tenth. Be careful! You will need to find the height of the triangles first!

15. Keira has a square poster that she is framing and placing on her wall. The poster has a diagonal 58 cm long and fits exactly inside the square frame frame. The width of the frame around the picture is 4 cm.

Determine and state the total area of the poster and also the area of the frame (shaded region) to the nearest tenth of a square centimeter.

16. Winston is building a brick walkway to his brand new pool. The cost of bricks is $28.72 per square meter. Winston budgeted himself to spend no more than $5000 for this project. How much money should he have left over after he purchases the bricks he needs?

17. Determine the following composite area in terms of pi.

Station 4: Area of Slanted Polygons

18. Determine the area of the following quadrilateral

1200 cm

19. Determine the area of a triangle ABC, whose vertices are A(-3,1) , B(1,3) and C(3,-2).

Mixed Practice20.Consider the pentagon inscribed in a circle whose sides lengths

are all 12 inches.

a. Calculate the area of the pentagon to the nearest hundredth

b. Determine and state the radius of the circle to the nearest hundredth.

c. Using your answers from a and b, determine the area of the shaded region.