Lesson 19: Unknown Area Problems on the Coordinate Plane
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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 , parallelogram . a. Write the ordered pairs of each of the vertices next to the vertex points. b. Draw a rectangle surrounding figure that has vertex points of and . Label the two triangles in the figure as and . c. Find the area of the rectangle. d. Find the area of each triangle. e. Use these areas to find the area of parallelogram . Lesson 19: Unknown Area Problems on the Coordinate Plane S.116 A STORY OF RATIOS Β© 2014 Common Core, Inc. All rights reserved. commoncore.org
Transcript of Lesson 19: Unknown Area Problems on the Coordinate Plane
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
S.116
A STORY OF RATIOS
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7β’3 Lesson 19
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
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7β’3 Lesson 19
Exercises
1. Find the area of triangle π΄π΄π΄π΄π΄π΄.
2. Find the area of quadrilateral π΄π΄π΄π΄π΄π΄π΄π΄ two different ways.
3. The area of quadrilateral π΄π΄π΄π΄π΄π΄π΄π΄ = 12 sq. units. Find π₯π₯.
Lesson 19: Unknown Area Problems on the Coordinate Plane
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7β’3 Lesson 19
4. The area of triangle π΄π΄π΄π΄π΄π΄ = 14 sq. units. Find the length of side π΄π΄π΄π΄.
5. Find the area of triangle π΄π΄π΄π΄π΄π΄.
Lesson 19: Unknown Area Problems on the Coordinate Plane
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7β’3 Lesson 19
Problem Set Find the area of each figure.
1.
2.
3.
4.
5.
6.
Lesson 19: Unknown Area Problems on the Coordinate Plane
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7β’3 Lesson 19
For Problems 7β9, draw a figure in the coordinate plane that matches each description.
7. A rectangle with area = 18 sq. units
8. A parallelogram with area = 50 sq. units
9. A triangle with area = 25 sq. units
Find the unknown value labelled as π₯π₯ on each figure.
10. The rectangle has an area of 80 sq. units.
11. The trapezoid has an area of 115 sq. units.
Lesson 19: Unknown Area Problems on the Coordinate Plane
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7β’3 Lesson 19
12. Find the area of triangle π΄π΄π΄π΄π΄π΄.
13. Find the area of the quadrilateral using two different methods. Describe the methods used and explain why they result in the same area.
14. Find the area of the quadrilateral using two different methods. What are the advantages or disadvantages of each method?
Lesson 19: Unknown Area Problems on the Coordinate Plane
S.122
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7β’3 Lesson 20
Lesson 20: Composite Area Problems
Classwork
Example 1
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.
Lesson 20: Composite Area Problems
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7β’3 Lesson 20
Example 2
Find the area of the figure that consists of a rectangle with a semicircle on top. Use 3.14 for ππ.
Exercise 2
Find the area of the shaded region. Use 3.14 for ππ.
Lesson 20: Composite Area Problems
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7β’3 Lesson 20
Example 3
Find the area of the shaded region.
Redraw the figure separating the triangles; then, label the lengths discussing the calculations.
Exercise 3
Find the area of the shaded region. The figure is not drawn to scale.
Lesson 20: Composite Area Problems
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7β’3 Lesson 20
Problem Set 1. Find the area of the shaded region. Use 3.14 for ππ.
2. The figure shows two semicircles. Find the area of the shaded region. Use 3.14 for ππ.
3. The figure shows a semicircle and a square. Find the area of the shaded region. Use 3.14 for ππ.
4. The figure shows two semicircles and a quarter of a circle. Find the area of the shaded region. Use 3.14 for ππ.
Lesson 20: Composite Area Problems
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7β’3 Lesson 20
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.
Lesson 20: Composite Area Problems
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7β’3 Lesson 20
8. Find the area of the shaded region.
9. a. Find the area of the shaded region.
b. Draw two ways the figure above can be divided in four equal parts.
c. What is the area of one of the parts in (b)?
10. The figure is a rectangle made out of triangles. Find the area of the shaded region.
Lesson 20: Composite Area Problems
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7β’3 Lesson 20
11. The figure consists of a right triangle and an eighth of a circle. Find the area of the shaded region. Use 227
for ππ.
Lesson 20: Composite Area Problems
S.129
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