L8.Finding Areas of Polygons Using the Coordinate Plane

Name: ____________________________________

Date: __________________

Finding the Areas of Polygons Using the Coordinate Plane

Algebra 1

Exercise #1: Graph the following set of points: A ( ?3, 1) , B (1, 6 ) , C ( 5, 1) . Find the area of ?ABC .

y

x

Exercise #2: Quadrilateral DEFG has vertices at D ( 6, 1) , E ( 2, 4 ) , F ( ?5, 4 ) , and G ( ?1, 1) .

(a) Graph DEFG and identify what type of quadrilateral it is.

y

(b) Calculate the area of DEFG.

x

(c) Calculate the perimeter of DEFG.

Some figures may be subdivided into smaller regions so that common area formulas can be used to

calculate the overall area.

Exercise #3: Find the area of the polygon ABCDEF with coordinates A ( 4, 0 ) , B ( 3,3) , C ( ?1, 3) ,

y

D ( ?4, 0 ) , E ( ?1, ? 3) , and F ( 3, ? 3) .

x

Algebra 1, Unit # 9 ¨C Measurement ¨C L8

The Arlington Algebra Project, LaGrangeville, NY 12540

To calculate the areas of more irregular shaped figures, it may be necessary to surround the figure with

a rectangle and subtract the areas outside of the graphed polygon.

Exercise #4: Find the area of ?ABC if it has vertices at A (1, 3) , B ( 5, 2 ) and C ( ?3, ? 3) .

y

x

Exercise #5: The quadrilateral ABCD has vertices with coordinates A (1, 4 ) , B ( 2, 3) , C ( 0, ? 3) and

D ( ?3, 1) . Graph ABCD and find its area.

y

x

Algebra 1, Unit # 9 ¨C Measurement ¨C L8

The Arlington Algebra Project, LaGrangeville, NY 12540

Name: ____________________________________

Date: __________________

Finding the Areas of Polygons Using the Coordinate Plane

Algebra 1 Homework

1. Calculate the perimeter and area of quadrilateral ABCD if it has

vertices at A ( ?3, 0 ) , B ( 3, 0 ) , C ( 3, 5 ) and D ( ?3,5) .

y

x

y

2. Calculate the perimeter and area of ?ABC whose coordinates

are A ( ?4, ? 3) , B ( 4, ? 3) and C ( 4, 3) .

x

y

3. Calculate the perimeter and area of parallelogram QRST whose

vertices are located at Q ( ?2, 3) , R ( 6, 3) , S ( 3, ? 1) and

T ( ?5, ? 1) .

x

Algebra 1, Unit # 9 ¨C Measurement ¨C L8

The Arlington Algebra Project, LaGrangeville, NY 12540

y

4. Calculate the area of pentagon EFGHI if it has vertices of

E ( 6, 1) , F ( 4, 3) , G ( ?2, 3) , H ( ?2, ? 1) , and J ( 4, ? 1) .

x

y

5. Trapezoid ABCD has vertices A(-2, 4), B(4, -2), C(-1, -4) and

D(-4, -1). Find the area of ABCD.

x

6. Trapezoid ABCD has vertices A ( ?1, 4 ) , B ( 2, 4 ) , C ( 4, ? 4 ) and D ( ?5, ? 4 ) .

y

(a) Find the area of ABCD.

x

(b) Using right triangle trigonometry, find m¡ÏD to the nearest degree.

Algebra 1, Unit # 9 ¨C Measurement ¨C L8

The Arlington Algebra Project, LaGrangeville, NY 12540

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