1/28/201610-3: Area of Polygons1 10-3: Area of Parallelograms G1.4.1: Solve multistep problems and construct proofs involving angle measure, side length,

05/03/23 10-3: Area of Polygons 1

10-3: Area of Parallelograms

G1.4.1: Solve multistep problems and construct proofs involving angle measure, side length, diagonal length,

perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.

G1.4.3: Describe and justify hierarchical relationships among quadrilaterals (e.g., every rectangle is a

parallelogram).G1.5.1: Know and use subdivision or circumscription

methods to find areas of polygons (e.g., regular octagon, nonregular pentagon).

Daily Quiz 5/19Betty is 4 feet tall and has to look up at an angle

of 23° to see the top of a tree. If she is 25 feet away from the tree, how tall is the tree (to the nearest foot)?

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AreaArea is the number of non-

overlapping squares inside a 2 dimensional shape. Area is always measured in ________ units, such as ___, ____ or _____.

Remember the word “square” is always said before the units.

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Area of a Rectangle PostulateIf a rectangle has length of L units,

width of W units and area of A square units, then A = _____.

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Area of a Rectangle

8 units

6 units

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Parallelograms

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Anatomy of a ParallelogramAnatomy of a Parallelogram

Any side of a parallelogram can be the base. The altitude of a parallelogram is a segment with its endpoints on the lines containing the bases, perpendicular to the bases. The height of the parallelogram is the length of the altitude.

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base 1

base 2

altitude

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base 1base 2

altitude

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What is the area of the parallelogram below and

why?13 feet

6 feet

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Area of a Parallelogram Formula

If the base of a parallelogram is b units,the height is h units and the area is A square units, then

A = ______.

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Calculate the area of the parallelogram below. Remember the

proper units.

10 mm

8 mm

21 mm

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What is the area of a parallelogram with vertices at (0,0), (2,3), (5,0) and (7,3)?

A. 10B. 14C. 15D. 21E. 35

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Determine the area of the figure below 2 different ways. Assume all angles are

right angles.3 cm 3 cm

4 cm

8 cm

4 cm

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Use this slide to make your second calculation.

3 cm 3 cm

4 cm

8 cm

4 cm

Parallelogram ABCD, with dimensions in inches, is shown in the diagram below. What is the area of the parallelogram, in square inches?A. 60B. 72 C. 180D. 240E. 260

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13

5 15D

C B

A

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Calculate the area of the shaded region below. The angles that appear to be right

angles are right angles.

24 in

34 in 8 in

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Calculate the area of the shaded (red) region below. The angles that appear to

be right angles are right angles.

5 in

6 in

2 in3 in

2 in

9.5 in

1 in4 in

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A floor has the dimensions shown below. How many square feet of tile are needed to cover the entire floor?

A. 50B. 95C. 160D. 190E. 220 19 feet

10 feet

5 feet

16 feet

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In the parallelogram below, lengths are given in inches. What is the area of the parallelogram, in square inches?

A. √94B. 7 √47C. 49D. 63E. 16 √47

7

√479

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Identify the quadrilateral with given vertices as a parallelogram,

rectangle or square and then determine its area.A(-4, -5), B(2, -5), C(4, -8), D(-2, -8)

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The measures of the angles of a triangle are in the ratio of 2x:3x:5x as illustrated below. What is the measure of the smallest angle?

A. 18B. 20C. 30D. 36E. 40

2x°5x°

3x°

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Assignment 10-3.1Pages 532 - 533,# 11 - 19 (odds)

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Assignment 10-3.2Pages 532 - 533,# 10 - 20 (evens)