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6-2 Area of a Parallelogram

Geogebra Area of a Parallelogram Proof Area of a Parallelogram Area of a parallelogram (2) Area vs. Perimeter Multiple Areas

Video Tutor Help Finding the measure of an angle Finding the area of parallelograms Finding the area of triangles Finding the area of trapezoids Finding circumference Finding the area of circles

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Video Tutor Help Area of a Parallelogram Identifying congruent trianglesIdentifying congruent triangles (6-2a) Khan Academy Area of polygons Brain Pop

Draw geometric shapes given the length of sides Lesson commentary for 'Draw geometric shapes given the length of sides' Draw triangles using given angles Lesson commentary for 'Draw triangles using given angles' Guided practice for 'Draw triangles using given angles' Determine if given measurements will allow you to create the appropriate shape Lesson commentary for 'Determine if given measurements will allow you to create the appropria... Guided practice for 'Determine if given measurements will allow you to create the appropriate... Draw a polygon using more than one condition Lesson commentary for 'Draw a polygon using more than one condition' Guided practice for 'Draw a polygon using more than one condition'

Find surface area of cubes and prisms by pulling them apart Lesson Slides Find surface area of cubes and prisms using formulas Lesson Slides Find missing dimensions using the volume formula Lesson Slides Choose the appropriate measurement for solving a problem Lesson Slides

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 6-2 Practice 6-2 Guided Problem Solving 6-2

Vocabulary Practice Vocabulary (Electronic) Flash Cards Percents Vocabulary 6A: Graphic Organizer Vocabulary 6B: Reading Comprehension Vocabulary 6C: Reading/Writing Math Symbols Vocabulary 6D: Visual Vocabulary Practice Vocabulary 6E: Vocabulary C Vocabulary 6F: Vocabulary Review Puzzle

Additional Lesson Examples Step-by-Step Examples Lesson 6-2

Lesson Readiness Lesson Quiz Problem of the Day Lesson 6-2

Perimeter is the distance around a polygon. To find the perimeter of any polygon, you add the lengths of all its sides. Since opposite sides of a parallelogram are equal in length, you can find a formula for the perimeter of a parallelogram. P = w + l + w + l = w + w + l + l = 2w + 2 l w l

Additional Example 1: Finding the Perimeter of Parallelograms A. Find the perimeter of the figure P = 2w + 2 l = 2(5) + 2(14) Perimeter of a parallelogram. = = 38 units Substitute 5 for w and 14 for l.

Additional Example 1: Finding the Perimeter of Parallelograms B. Find the perimeter of the figure. P = 2w + 2 l = 2(16) + 2(20) Perimeter of a parallelogram. = = 72 units Substitute 16 for w and 20 for l.

6 11 Partner Share! Example 1 A. Find the perimeter of the figure. P = 2w + 2 l = 2(6) + 2(11) Perimeter of a parallelogram. = = 34 units Substitute 6 for w and 11 for l.

13 5 Partner Share! Example 1 B. Find the perimeter of the figure. P = 2w + 2 l = 2(5) + 2(13) Perimeter of a parallelogram. = = 36 units Substitute 5 for w and 13 for l.

The area of a plane figure is the number of unit squares needed to cover the figure. The base of a parallelogram is the length of one side. The height is the perpendicular distance from the base to the opposite side. Height Side Base

While perimeter is expressed in linear units, such as inches (in.) or meters (m), area is expressed in square units, such as square feet (ft 2 ). You can cut a parallelogram and shift the cut piece to form a rectangle whose base and height are the same as those of the original parallelogram. The same number of unit squares are needed to cover the two figures. So a parallelogram and a rectangle that have the same base and height have the same area.

Since the base and height of a rectangle are the same as its length and width, the formula for the area of a rectangle can also be written as A = lw. Helpful Hint

A. (–1, –2), (2, –2), (2, 3), (–1, 3) A = 15 units 2 A = 3 5 A = bh Additional Example 2: Using a Graph to Find Area Graph and find the area of the figure with the given vertices. Area of a rectangle. Substitute 3 for b and 5 for h.

The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base. Caution!

B. (0, 0), (5, 0), (6, 4), (1, 4) Additional Example 2: Using a Graph to Find Area A = 20 units 2 A = 5 4 A = bh Area of a parallelogram. Substitute 5 for b and 4 for h. Graph and find the area of the figure with the given vertices.

Partner Share! Example 2 A. (–3, –2), (1, –2), (1, 3), (–3, 3) A = 20 units 2 A = 4 5 A = bh Area of a rectangle. Substitute 4 for b and 5 for h. x y (–3, –2) (1, –2) (1, 3) (–3, 3) 4 5 Graph and find the area of the figure with the given vertices.

B. (–1, –1), (3, –1), (5, 3), (1, 3) Partner Share! Example 2 Graph the figure with the given vertices. Then find the area of the figure. (5, 3) x y (–1, –1) (3, –1) (1, 3) 4 4 A = 16 units 2 A = 4 4 A = bh Area of a parallelogram. Substitute 4 for b and 4 for h.

Area of a Parallelogram altitude base The height is the length of the altitude, a line segment perpendicular to the base with endpoints on the base and the side opposite the base. The base can be any side of the parallelogram. The area A of a parallelogram is the product of any base b and its height h. A= bh

Teaching Tip Do not confuse the side of a quadrilateral for its height. The height of a quadrilateral is the perpendicular distance from the figure’s base to its opposite side.

Example 5-1a Find the area of the parallelogram. The base is 3 meters. The height is 3 meters. Area of a parallelogram Replace b with 3 and h with 3. Multiply. Answer: The area is 9 square meters. Find Areas of Parallelograms

Example 5-1a Find the area of the parallelogram. The base is 4.3 inches. The height is 6.2 inches. Area of a parallelogram Replace b with 4.3 and h with 6.2. Multiply. Answer: The area is square inches. Find Areas of Parallelograms

Example 1-1a Find the area of the parallelogram. The base is 7 centimeters. The height is 2 centimeters. Area of a parallelogram Replace b with 7 and h with 2. Multiply. Answer: The area is 14 square centimeters. Find the Area of a Parallelogram

Example 1-1b Find the area of the parallelogram. Answer: