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Discovering Area of a Circle

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**Area of a Circle Discovery**

For Learning to Happen: Pay close attention to this lesson. Listen to my instructions to discover the area of a circle formula.

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**Area of a Circle Discovery**

You are going to get a white half sheet. Label the circumference, diameter and radius on your circle.

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**Area of a Circle Discovery**

Circumference Diameter Radius Carefully cut out the circle on the black line.

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**Area of a Circle Discovery**

Cut out the circle on the bolded lines. Cut along the diameter to cut the circle in half. You should have 2 halves.

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**Area of a Circle Discovery**

Start from the diameter and cut the 4 pieces. DO NOT CUT IT TO THE EDGE! Open the semicircles and bend them out so they look like 4 connected triangles.

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**Area of a Circle Discovery**

Fit the 4 triangles together so that as one is facing up, the other is facing down. Tape these pieces together on your blue study guide handout. Make sure your words on facing up! radius Circumference

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**Area of a Circle Discovery**

Answer the following questions. What does your new figure look like? Parallelogram 2a. Draw your answer here. Label base & height 2b. How do you find the area of a parallelogram? Base x Height height base

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**Area of a Circle Discovery**

3. Draw your area of a circle figure below. In knowing that you need to find the base and height of your new figure to calculate the area, what is the height of your new figure? Label your picture. 4. What is the bottom base of your new figure? Label your picture above. Hint: Half of the circumference. Height = radius pi x radius

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**Area of a Circle Discovery**

If you know the base and height of your new figure can you find the area? Take your base and multiply it by your height. Show your work! 6. Simplify your formula. 7. Write out how you find the area of a circle. Pi times radius squared.

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**Area of a Circle Discovery**

Here is what we just did: We labeled everything. Area = base times the height. r r radius Circumference is the distance around the circle. We cut our circle in half making two pieces.

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**Area of a Circle Discovery**

Watch what happens when we use a circle with 16 triangles instead of using a circle with 8 triangles. r r Notice that with more triangles the figure begins to really resemble a parallelogram. Area of a parallelogram is base times height.

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**Area of a Circle Discovery**

Take out a calculator to try to solve the following problems on area of a circle.

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**Area of a Circle Discovery**

6 in. Find the area of the circle.

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**Area of a Circle Discovery**

11 m. Find the area of the circle.

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**Find the area of the circle.**

Area of a Circle Discovery What is the radius if the diameter is 10 ft? 10 ft. Find the area of the circle.

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**Take out your study guide!**

Area of a Circle Discovery That's all Folks! The End! Take out your study guide! That’s all folks

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**copyright©amberpasillas2010**

Area of a Circle #7 6 in = 3.14 or 22 7 copyright©amberpasillas2010

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**Given the Radius of a Circle**

#8 Given the Radius of a Circle Round to the nearest hundredths place and include units! 5 ft Find the Circumference Find the Area copyright©amberpasillas2010

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**Use this as a master to give to students **

for the interactive discovery of a circle along with a copy of the worksheet. Student materials for interactive discovery of a circle: Copy of circle pictured above, copy of area worksheet in this folder, scissors & tape.

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**Area of a Circle Area of a Circle**

Follow the teacher directions and cut the circle out. Area of a Circle Follow the teacher directions and cut the circle out.

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**TEACHER NOTE: Give each student a copy of this page**

TEACHER NOTE: Give each student a copy of this page. The master copy is in the folder as a pdf.

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Objective Students will solve practical area and perimeter problems involving composite plane figures.

Objective Students will solve practical area and perimeter problems involving composite plane figures.

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