Dorchester 2 04-15-2025 Area of Regular Polygon

Open Ended

Determine the Wordplexers.

Write the number, then the phrase.

Include the examples in your response.

Examples: 6-bad feedback; 7-splitting headache

Area & Probability – Learning Objectives

By the end of this unit, I can:

✅ Find the area of any two-dimensional or composite figure
✅ Use trigonometric ratios and special right triangles to find area
✅ Determine the area of regular polygons using formulas and trig
✅ Calculate geometric probability using shaded vs. total area
✅ Describe events using sample space, union, and complement
✅ Classify events as mutually exclusive or not
✅ Apply the Addition Rule to find the probability of unions
✅ Determine if events are independent or dependent
✅ Use the Multiplication Rule to find the intersection of independent events

Steps to Remember for Area of Composite Figures

Key Points:

1. Break complex shapes into basic ones (triangles, rectangles, circles)

2. Label all dimensions before calculating

3. Add areas together to find the total

4. If part is missing (shaded region), subtract the smaller shape from the larger.

Today's Objectives:

• I can find the area of composite and regular polygons.

• I can use geometric probability to solve real-world problems.

​Quick Review

Multiple Select

Which of these figures are regular polygons?

Multiple Choice

REGULAR in Maths means...

• Normal

• Two sides have the same length

• All sides are equal and all angles are equal

• It has right angles

Draw

Find the area of the figure.

Draw process or put your process in chat.

Write the total area in the bottom right corner with units.

Draw

Area of the shaded region.

Draw process or put your process in chat.

Write the total area in the bottom right corner with units.

Multiple Choice

Find a.

• 5

• √2

• 5√2

• 2

Dropdown

In a 30-60-90 right triangle, to find the measure of the long leg, you take the ​​

Select answer

and ​ ​

Select answer

by ​

Select answer

.​

Multiple Choice

If the leg of a 45-45-90 triangle is 7 cm long, then its hypotenuse is _____ cm.

• 7√2
• 49√2
• 7
• 7√7

Dropdown

In a 45-45-90 right triangle, to find the measure of a leg, you take the ​

Select answer

and ​

Select answer

by ​

Select answer

.​

Match

Match the following for finding sides in a 30-60-90 right triangle.

• Short Leg

• Hypotenuse

• Long Leg

Half of the hypotenuse

Double the short leg

Short leg times square root of 3

• Half of the hypotenuse

• Double the short leg

• Short leg times square root of 3

Match

Match the following for a 30-60-90 right triangle

• Short Leg

• Long Leg

• Hypotenuse

Opposite the 30° angle.

Opposite the 60° angle.

Opposite the right angle.

• Opposite the 30° angle.

• Opposite the 60° angle.

• Opposite the right angle.

Labeling

Label each of the following.

Drag labels to their correct position on the image

Short Leg

Long Leg

Hypotenuse

Multiple Choice

Find the value of y.

• 8

• 4

• 2√3

• 8√3

Multiple Choice

Find the value of y.

• 11√2
• 11
• 22
• (11√2)/2

Multiple Choice

Find the area of the composite figure

• 3 ft²

• 51.5 ft²

• 32 ft²

• 44 ft²

Area of Regular Polygons

Essential Question:
How can I find the area of ANY regular polygon?

​Steps to Find the Area of Regular Polygons

Open Ended

Cole is in an exhibit room of a local museum. The room is shaped like a regular hexagon.

Each side of the hexagon is 6.25 meters. Find the area of the room. Solve this problem. Round to the nearest tenth.

Open Ended

Jayden is baking a cake for a birthday party. She needs to figure out how much frosting or decorations are needed to cover the surface of the cake. The top of the cake is shaped like a regular decagon. Each side of the decagon is 2.5 inches. Find the area of the cake top. Round to the nearest hundredth.

Open Ended

Garret is covering a seat for a doll. The seat is shaped like a regular heptagon. Each side of the heptagon is 6.75 centimeters. Find the area of the seat, round to the nearest hundredth.

Open Ended

Aaliya is building a plant stand out of wood. The top of the plant stand is shaped like a regular decagon. Each side of the decagon is 2.7 inches. Find the area of the top of the plant stand. Round to the nearest hundredth.

Open Ended

Destiny is visiting a butterfly garden. The garden is shaped like a regular octagon. Each side of the octagon is 5.4 meters. Find the area of the butterfly garden. Round to the nearest hundredth.

Fill in the Blanks

7.  Heather is building a pond for a local park. The pond is shaped like a regular dodecagon. Each side of the dodecagon is 4.25 yards. Find the area of the pond.  Do NOT round your answer.  

yds²

Fill in the Blanks

Shina is setting out a serving plate for dinner. The plate is shaped like a regular pentagon. Each side of the pentagon is 6.25 inches. Find the area of the plate. Round to the nearest hundredth.

in.²

Poll

After exploring, working on examples, and working independently, I feel confident using the apothem to find the area of regular polygons.

Independent Practice
study.com https://study.com/member/classrooms/share.html?classroom=copper-fish-2146&assignment=10676634

• Watch the video, read the lesson, and complete the 5 questions.

• Turn in a pic of work for the quiz to Schoology.

• Be sure ALL problems that require calculations are clearly visible