Download 7.6 Polygons and Area and Perimeter Name

7.6 Polygons and Area and Perimeter
Name ________________________ Per ____
Review
1. Determine whether each pair of lines are parallel, perpendicular or neither and explain.
A.
B.
C.
E.
F.
D.
G.
Equilateral Triangle ______________________Scalene Triangle _____________________
Isosceles Triangle ________________________________________________________
Acute Triangle___________________________Obtuse Triangle____________________
Right Triangle ___________________________________________________________
Parallelogram ____________________________________________________________
Rectangle _______________________________________________________________
Square __________________________________________________________________
Trapezoid _______________________________________________________________
Bases of a trapezoid _______________________________________________________
Perimeter of a figure (not a circle) _____________________________________________
Base and height of a polygon must meet at ________________________
Area of a Triangle 𝐴 =
𝑏ℎ
2
𝑜𝑟 𝐴 =
1
2
𝑏ℎ
Area of a parallelogram and rectangle 𝐴 = 𝑏ℎ
Area of a square 𝐴 = 𝑏ℎ 𝑜𝑟 𝐴 = 𝑠 ∙ 𝑠 𝑜𝑟 𝐴 = 𝑠 2
1
Area of Trapezoid 𝐴 = 2 (𝑏1 + 𝑏2 )ℎ
Graph triangle ABC using each set of given points. Determine if triangle ABC is scalene,
isosceles, or equilateral. Justify your answer!
2. A( 3, 1), B( 3, 3), C(1, 0)
3. A(8, 5), B(8, 1), C(4, 3)
4. A(5, 8), B(5, 2), C( 3, 5)
Graph triangle ABC using each set of given points. Determine if triangle ABC is a right triangle,
an acute triangle, or an obtuse triangle.
5. A(0, 4), B(4, 5), C(1, 0)
6. A( 6, 1), B( 6, 4), C(4, 0)
7. A( 5, 7), B(7, 7), C(1, 4)
Graph quadrilateral ABCD using each set of given points. Determine if quadrilateral ABCD can
be best described as a trapezoid, a square, or a rectangle. Justify your answer!
8. A( 4, 2), B(2, 4), C(8, 2),
D(2, 8)
9. A(0, 6), B(3, 4), C( 1, 2),
D( 4, 0)
10. A(1, 0), B(2, 4), C(10, 2),
D(5, 1)
Determine the area and perimeter of each image on the coordinate plane. Round your answer to
the nearest hundredth, if necessary. Show your work!
11. Rectangle WXYZ
12. Square AFTZ
13. Triangle ABC
14. Triangle DEF
15. Parallelogram STVZ
16. Trapezoid ABCD
17. Figure PQRST
18. Figure ABCDEFGH
Write the slope-intercept equation for the lines that are parallel and perpendicular to
𝒚 = −𝟑𝒙 + 𝟕 that goes through (12, -2)
19. Equation of parallel line
20. Equation of perpendicular line
Answer Key:
1. A) parallel B) neither C) perpendicular D) parallel E) perpendicular F) neither G) parallel
2. Because each of the side lengths
are different, triangle ABC is
scalene.
3.
4. Because sides AC and BC are equal,
Because sides AC and BC
triangle ABC is isosceles.
are equal, triangle ABC is isosceles.
5.
Slope segment AB:
Slope segment BC:
Slope segment AC:
The slope of line segments AB and AC are negative reciprocals and therefore form a right angle.
Triangle ABC is a right triangle.
6. Triangle ABC is not a right triangle. Because
all three angles are less than 90°,
triangle ABC is an acute triangle.
7. Triangle ABC is not a right triangle. Because one
angle is greater than 90°, triangle ABC.
is an obtuse triangle
8. All sides are congruent and the slopes are
1 or -1 which are opposite
reciprocals of each other
which means the angles
are right angles.
15. The perimeter is approximately 24.2
units. The area is 35 square units.
16. The perimeter is approximately 19.83
units. The area is 22.5 square units.
17. The perimeter is approximately 19.22
units. The area is 24 square units.
18. The perimeter is approximately 23.66
9. The slopes of the line segments are opposite
reciprocals. This means the
line segments are
perpendicular, which means
the angles must be right
angles. Also, the opposite
sides have the same slope,
so the opposite sides are
parallel. Finally, the opposite sides are
congruent. Quadrilateral ABCD can best be
described as a rectangle.
10. The slopes of the line segments do not all
have a negative reciprocal
relationship, so the line
segments are not all
perpendicular. This means
the angles of this figure
are not all right angles.
Only one set of opposite
sides have the same slope, so only one set of
opposite sides are parallel. Quadrilateral ABCD
can best be described as a trapezoid.
11. The perimeter is approximately 13.42
units. The area is 10 square units.
12. The perimeter is approximately 16.97
units. The area is 18 square units.
13. The perimeter is approximately 16.28
units. The area is 7 square units.
14. The perimeter is approximately 38.55
units. The area is 67.5 square units.
units. The area is 22 square units.
19. Equation of the parallel line is
Y = -3x+34
20. Equation of perpendicular line is
1
𝑦 = 3𝑥 − 6