Part A: Explore

Geometry Online: Instructor Content Lesson 01: Geometry Basics Part A: Explore

Watch topic videos, fill in guided notes and examples, and complete Checkpoints.

Two-Dimensional Figures and Formulas

Refer to your student’s print out or Student Worktext for this lesson section and video. Students will complete the guided notes section as they watch the video.

two-dimensional
perimeter; area
- distance around; circumference
- space
composite

dashed
Formula Sheet
Combine

Examples

Refer to your student’s print out or Student Worktext for each example. Students will follow along and complete the examples as they watch the videos.

Example 1

Implement

Shapes: rectangle, semi-circle, triangle, trapezoid

Formulas:

$A = l w, A = \frac{1}{2} π r^{2}, A = \frac{1}{2} b h, A = \frac{h}{2} (b_{1} + b_{2}) C = \frac{1}{2} (2 π r) = πr A = \frac{1}{2} π r^{2} = \frac{π}{2} {(1.5)}^{2} = 1.125 π sq units A = \frac{1}{2} b h = \frac{1}{2} (8) (1.5) = 6 sq units A = \frac{h}{2} (b_{1} + b_{2}) = \frac{1.5}{2} (3 + 1.5) = 3.375 sq units Total Area = 24 + 6 + 3.375 + 1.125 π TA = 33.375 + 1.125 π sq units C = π r = π (1.5) = 1.5 π units P = 4 (4.27) + 1.5 + 8 + 1.5 π = 26.5 + 1.5 π units$

Explain

Rational and irrational numbers cannot be added together here. Pi is an irrational number with an estimated value of 3.14 but the directions say to leave in terms of pi. (See A1:PSM for more about number classification)

Example 2

F = 2
E = D = 12 – 5 = 7
C = 10 – D = 10 – 7 = 3
B = 11 – (8 – 2) = 5

Area 1 = (5)(3) = 15 sq units
Area 2 = (11)(7) = 77 sq units
Area 3 = (2)(12) = 24 sq units

Have your student mark their figure for things they know have the same length. Their figure does not have to have the same markings as the key.

Checkpoint

To continue past this checkpoint, students should confidently and correctly answer this problem.

$A = \frac{1}{2} b h 120 = \frac{1}{2} (b) (8) 120 = 4 b b = 30 feet$

triangle base = width of rectangle

A = lw
330 = 30l
l = 22 feet

Q: What formulas will you need for this problem?
A: Area of a rectangle and area of a triangle

Q: How are the two figures related?
A: The base of the triangle is the width of the rectangle, so they will be the same length.

Q: Is it possible to determine the perimeter for the composite figure? Explain.
A: No, because the sides of the triangle are unknown.

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