1/28/ : Area of Polygons3 Area Area 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. Area 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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06/17/22 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).
Transcript
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)?
05/03/23 10-3: Area of Polygons 3
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.
05/03/23 10-3: Area of Polygons 4
Area of a Rectangle PostulateIf a rectangle has length of L units,
width of W units and area of A square units, then A = _____.
05/03/23 10-3: Area of Polygons 5
Area of a Rectangle
8 units
6 units
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Parallelograms
05/03/23 10-3: Area of Polygons 7
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.
05/03/23 10-3: Area of Polygons 8
base 1
base 2
altitude
05/03/23 10-3: Area of Polygons 9
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
05/03/23 10-3: Area of Polygons 13
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
05/03/23 10-3: Area of Polygons 14
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
05/03/23 10-3: Area of Polygons 20
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
05/03/23 10-3: Area of Polygons 21
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
05/03/23 10-3: Area of Polygons 22
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
05/03/23 10-3: Area of Polygons 23
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)
05/03/23 10-3: Area of Polygons 24
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?
