Unknown Area Problems on the Coordinate Plane

Examples, videos, and solutions to help Grade 7 students learn how to find the areas of triangles and simple polygonal regions in the coordinate plane.

New York State Common Core Math Grade 7, Module 3, Lesson 19

Worksheets for Grade 7

Lesson 19 Student Outcomes

• Students find the areas of triangles and simple polygonal regions in the coordinate plane with vertices at grid points by composing into rectangles and decomposing into triangles and quadrilaterals.

Closing

Vocabulary:
quadrilateral, parallelogram, trapezoid, rectangle, square, altitude and base of a triangle, semicircle, diameter of a circle.

Area formulas:
Area of parallelogram = Base x Height
Area of rectangle = Base x Height
Area of a triangle = 1/2 x Base x Height
Area of a trapezoid = 1/2 x (Base 1 + Base 2) x Height
Area of a circle = π x r²

Lesson 19 Classwork

Example: Area of a Parallelogram
The coordinate plane below contains figure P, parallelogram ABCD.
a. Write the ordered pairs of each of the vertices next to the vertex points.
b. Draw a rectangle surrounding figure P that has vertex points of A and C. Label the two triangles in the figure as S and T.
c. Find the area of the rectangle.
d. Find the area of each triangle.
e. Use these areas to find the area of parallelogram ABCD.

The coordinate plane below contains figure R, a rectangle with the same base as the parallelogram above.
f. Draw triangles S and T next to R so that you have a rectangle that is the same size as the one you created on the first coordinate plane.
g. Find the area of rectangle R.
h. What do figures R and P have in common?

Exercises

1. Find the area of triangle ABC.
   
2. Find the area of quadrilateral ABCD two different ways.
   
3. The area of quadrilateral ABCD = 12 sq. units. Find x.
   
4. The area of triangle ABC = 14 sq. units. Find the length of side BC.
   
5. Find the area of triangle ABC.

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