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7β’3 Lesson 19
Lesson 19: Unknown Area Problems on the Coordinate Plane
Classwork
Example: Area of a Parallelogram
The coordinate plane below contains figure ππ, parallelogram π΄π΄π΄π΄π΄π΄π΄π΄.
a. Write the ordered pairs of each of the vertices next to the vertex points.
b. Draw a rectangle surrounding figure ππ that has vertex points of π΄π΄ and π΄π΄. Label the two triangles in the figure as ππ and ππ.
c. Find the area of the rectangle.
d. Find the area of each triangle.
e. Use these areas to find the area of parallelogram π΄π΄π΄π΄π΄π΄π΄π΄.
Lesson 19: Unknown Area Problems on the Coordinate Plane
The coordinate plane below contains figure π π , a rectangle with the same base as the parallelogram above.
f. Draw triangles ππ and ππ and connect to figure π π so that you create a rectangle that is the same size as the rectangle you created on the first coordinate plane.
g. Find the area of rectangle π π .
h. What do figures π π and ππ have in common?
Lesson 19: Unknown Area Problems on the Coordinate Plane
Find the composite area of the shaded region. Use 3.14 for ππ.
Exercise 1
A yard is shown with the shaded section indicating grassy areas and the unshaded sections indicating paved areas. Find the area of the space covered with grass in units2.
5. Jillian is making a paper flower motif for an art project. The flower she is making has four petals; each petal is formed by three semicircles as shown below. What is the area of the paper flower? Provide your answer in terms of ππ.
6. The figure is formed by five rectangles. Find the area of the unshaded rectangular region.
7. The smaller squares in the shaded region each have side lengths of 1.5 m. Find the area of the shaded region.