Finding Area - Circles and polygons

Finding Area - Circles and Polygons

Our "pointless" lesson is actually SUPER important! Ready? Let's go!

First, let's review Pi

Not the kind you eat, the irrational number. You can express it as a fraction: 22/7 OR round it to 3.14

Now, let's review about circles...

Multiple Select

The circumference of a circle is... (select 2!)

• C = π r

• C = π r²

• C = 2 π r

• C = π d

Area of Polygons!

• A quadrilateral is a shape with FOUR (4) sides (square, trapezoid, rectangle, etc)

• Area of rectangle or parallelogram: A = b x h (base times height)

• Area of a triangle: A = 1/2 (b x h) (half of base times height)

• Area of trapezoid: A = 1/2 (h x (b1 + b2)) (half of height times sum of base 1 and base 2)

Multiple Choice

A quadrilateral is...

• a shape with 3 sides

• a shape with 4 sides

• a common shape

• a type of trapezoid

Multiple Choice

To find area of a parallelogram (a type of quadrilateral) the formula is...

• A = bh

• A = 1/2 (bh)

• A = π r

Multiple Choice

To find area of a triangle it is:

• A = b · h (base times height)

• A = 1/2 b · h (half of base times height)

Multiple Choice

To find area of a rectangle it is:

• A = b · h (base times height)

• A = 1/2 b · h (half of base times height)

Finding the area of a shaded region

• FIRST, find the area of the BIGGER shape

• THEN, find the area of the SMALLER shape that is NOT shaded (darker)

• SUBTRACT the smaller (not shaded) shape from the bigger shape to find the shaded area (the area that is darker)

Finding the area of a composite figure

• FIRST, divide and SEPARATE into smaller shapes. (like the semicircle and triangle in the example)

• THEN, find the area of EACH INDIVIDUAL shape (like the semicircle and then the triangle in the example)

• ADD the area of all the smaller shapes together to find the total area. In the example, 14.1 + 33 = total area of 47.1

NOTE: Get some paper handy so you can solve these questions! Your answers will be graded.

Multiple Choice

Mike installed the window shown with base of 1.5 ft and rectangle height of 2ft. How many square feet is the window? Use 3.14 for pi. Round to the nearest tenth.

• 39 ft²

• 3.9 ft²

• 7.9 ft²

• 1.9 ft²

How to find the area:

• Find area of the Rectangle (base times height) which is 1.5 x 2 = 3

• Find the area of the semicircle (.5)x(3.14)x(.75)(.75) = 0.88 (0.9 when rounded)

• Add the two areas together: 3 + 0.9 = 3.9 sq ft

Multiple Choice

A triangle is cut from a rectangle. The base of the rectangle is 11 ft and height is 6 ft. The base of the triangle is 4 ft. Determine the area of the shaded region.

• 66 ft²

• 24 ft²

• 54 ft²

• 12 ft²

How to find area:

• Find area of the big rectangle (11 x 6 = 66)

• Find area of the triangle (0.5 x 4 x 6 = 12)

• Subtract the triangle area from the rectangle area (66 - 12 = 54)

• So the answer is 54 sq ft

Multiple Choice

What is the area of a circle with a radius of 7?

• 153.9

• 49

• 44

• 22

Multiple Choice

Determine the area of the figure. Round to the nearest tenth if necessary

• 64 cm²

• 54 cm²

Multiple Choice

Determine the area of the figure. Round to the nearest tenth if necessary

• 64 m²

• 169 m²

Multiple Choice

Determine the area of the figure. Round to the nearest tenth if necessary

• 220.5 cm²

• 120 cm²

Multiple Choice

Determine the area of the figure. Round to the nearest tenth if necessary

• 75 cm²

• 77 cm²

Great job! I'll grade what you've done in these slides. Now you're done!

H

-Mrs. Hobbs