Geometry Unit 5, Lesson 7 Practice

Study Notes

Areas of Circles

The area of a circle is calculated using the formula ( A = \pi r^2 ).
Example: For a circle with a radius resulting in an area of 49π square feet, the radius is 7 feet.

Perimeter of Rectangles

The perimeter of a rectangle is determined by the lengths of its sides.
For circles with an area of 196π square units, example calculations show a total rectangle perimeter of 168 units.

Area of Shaded Regions

Shaded areas often require subtracting circles from rectangles.
In one example, the area of the shaded region was (4 - π) ft².

Circular Patio

The area of a circular patio can be approximated based on its diameter.
A patio with a diameter of 20 feet has an area of approximately 314 square feet.

Sectors of Circles

When a circle is divided into sectors, the area of one sector can be found by dividing the total area by the number of sectors.
A circle with a radius of 12 mm divided into 20 sectors yields an area of approximately 22.6 square mm per sector.

Sector Area Calculation

The area of a 90° sector is proportional to the total area of the circle.
A sector with an area of 36π square inches corresponds to a radius of 12 inches.

Shaded Sector Areas

The area of a shaded sector can also be expressed in terms of π.
For a given circle, one example shows an area of 12π ft² for the shaded sector.

Sector Area from Diameter

The area of sectors can be calculated using knowledge of the diameter and the measure of the arc.
For circle O with a diameter of 15 cm and an arc measure of 180°, the area of sector TOP is 28.125π square centimeters.

Shaded Segment Area

Calculating the area of a shaded segment often involves combining Circle and triangle area formulas.
An example calculation indicates a shaded segment area of approximately 22.1 cm².

Complex Areas

Some areas may involve more intricate calculations, factoring in multiple geometrical shapes.
In a complex case, the area of a shaded region was computed to be (243π + 162) ft².

Description

Test your knowledge of calculating areas of circles and sectors with this practice quiz. Each question provides a scenario where you need to apply your understanding of geometry concepts to find the areas and perimeters needed. Get ready to sharpen your skills in evaluating circle areas and more!