Lesson 19: Unknown Area Problems on the Coordinate Plane

7•3 Lesson 19

Lesson 19: Unknown Area Problems on the Coordinate Plane

Classwork

Example: Area of a Parallelogram

The coordinate plane below contains figure 𝑃𝑃, parallelogram 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴.

a. Write the ordered pairs of each of the vertices next to the vertex points.

b. Draw a rectangle surrounding figure 𝑃𝑃 that has vertex points of 𝐴𝐴 and 𝐴𝐴. Label the two triangles in the figure as 𝑆𝑆 and 𝑇𝑇.

c. Find the area of the rectangle.

d. Find the area of each triangle.

e. Use these areas to find the area of parallelogram 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴.


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7•3 Lesson 19

The coordinate plane below contains figure 𝑅𝑅, a rectangle with the same base as the parallelogram above.

f. Draw triangles 𝑆𝑆 and 𝑇𝑇 and connect to figure 𝑅𝑅 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 𝑅𝑅.

h. What do figures 𝑅𝑅 and 𝑃𝑃 have in common?


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7•3 Lesson 19

Exercises

1. Find the area of triangle 𝐴𝐴𝐴𝐴𝐴𝐴.

2. Find the area of quadrilateral 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 two different ways.

3. The area of quadrilateral 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 = 12 sq. units. Find 𝑥𝑥.


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7•3 Lesson 19

4. The area of triangle 𝐴𝐴𝐴𝐴𝐴𝐴 = 14 sq. units. Find the length of side 𝐴𝐴𝐴𝐴.



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7•3 Lesson 19

Problem Set Find the area of each figure.

1.

2.

3.

4.

5.

6.


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7•3 Lesson 19

For Problems 7–9, 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 𝑥𝑥 on each figure.

10. The rectangle has an area of 80 sq. units.

11. The trapezoid has an area of 115 sq. units.


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7•3 Lesson 19


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?


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7•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.


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7•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.


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7•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.


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7•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.


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7•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.


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7•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.


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7•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.


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Lesson 19: Unknown Area Problems on the Coordinate Plane