Lesson 24-2
Area of Polygons on a Coordinate Plane
ACTIVITY 24
continued
Learning Targets:
Use coordinate geometry to identify locations on a plane.
Graph points in all four quadrants.
Solve problems involving the area of parallelograms, trapezoids, and
triangles.
My Notes
•
•
•
SUGGESTED LEARNING STRATEGIES: Visualization, Sharing and
Responding, Create a Plan, Create Representations
There are three different types of triangles in the scale drawing of Zena’s
mural design. They are shown in the first quadrant section of the mural.
Remember, each square on the grid represents 1 square foot.
y Triangle
2
Triangle
3
Triangle
1
x
© 2014 College Board. All rights reserved.
1. Find the area of each triangle. Justify your answers.
a. gray triangle 1
b. white triangle 2
c. dark blue triangle 3
Activity 24 • Polygons on the Coordinate Plane
309
Lesson 24-2
Area of Polygons on a Coordinate Plane
Activity 24
continued
My Notes
2. The endpoints of triangle ABC on a coordinate grid plane are
A(-3.5, 4), B(-3.5, -1), and C(2.5, -1).
a. Use the My Notes section to create a coordinate grid. Draw the
triangle on the coordinate grid.
b. What is the area of triangle ABC? Explain.
3. There are four congruent white trapezoids in the original mural
design. One of the trapezoids is shown on the grid.
y E
Math Tip
T
P
D
Remember, two sides of a polygon
intersect at a vertex. The plural of
vertex is vertices.
x
a. What are the coordinates of the vertices of the trapezoid?
Remember, the area, A, of a
trapezoid with height h and bases
b1 and b2 is A = 1 × h ×(b1 + b2 ) .
2
c. What is the area of the trapezoid in the mural design? Explain
your reasoning.
d.How much of the mural area do the four white trapezoids make up?
310 Unit 5 • Geometric Concepts
© 2014 College Board. All rights reserved.
Math Tip
b. What is the height of the trapezoid in the mural design? What are
the lengths of the bases?
Lesson 24-2
Area of Polygons on a Coordinate Plane
Activity 24
continued
My Notes
The complete model of Zena’s mural design is shown.
y X
W
x
Y
Z
4. Look back at Items 1 and 3.
a. What is the total area of the four white triangles? Explain your
reasoning.
© 2014 College Board. All rights reserved.
b. What is the total area of the white trapezoids and the white
triangles? Explain your reasoning.
c. Each can of white paint costs $42.75 and will cover 50 square feet.
How much will the white paint cost for the mural? Explain your
reasoning.
5. Construct viable arguments. There is an octagon in the center of
the mural. Use what you know about the area of triangles and
rectangles to find the area of the octagon. Explain your reasoning. Activity 24 • Polygons on the Coordinate Plane 311
Lesson 24-2
Area of Polygons on a Coordinate Plane
Activity 24
continued
My Notes
Check Your Understanding
Use the coordinate grid for Items 6–9.
6. Trapezoid ABCD has vertices at A(1, 3),
B(-2, 3), C(-3, 2), and D(4, 2). Draw
trapezoid ABCD.
7. What is the length of the bases of
trapezoid ABCD?
y 5
5
–5
x
8. What is the height of trapezoid ABCD?
9. Find the area of trapezoid ABCD.
–5
LESSON 24-2 PRACTICE
Use the coordinate grid for Items 10–13.
10. Triangle PQR has vertices at
P(-1, 1), Q(-1, 3), and R(2.5, -2).
Draw triangle PQR.
11. What is the length of the base of
triangle PQR?
y 5
5
–5
x
12. What is the height of triangle PQR?
13. Find the area of triangle PQR.
–5
14. What are the coordinates of the vertices
of this trapezoid?
y 5
D
15. What are the lengths of the bases of the
trapezoid?
16. What is the height of the trapezoid?
17. Find the area of the trapezoid if each
square on the grid represents 1 square
meter.
C
5
–5
E
F
–5
18. Make sense of problems. The trapezoid in Items 14–17 is a scale
model of a deck that Gayle is planning to build. The material for the
deck costs $4.35 per square meter. What will be the cost of the deck?
19. Construct viable arguments. A right triangle has vertices at
(16.5, 12), (16.5, -8), and (-10, 12). Explain how to find the area of
the triangle without drawing the triangle on a coordinate grid.
312 Unit 5 • Geometric Concepts
x
© 2014 College Board. All rights reserved.
Use trapezoid CDEF for Items 14–18.