Download GEOMETRY WORKSHEET

GEOMETRY WORKSHEET
Name ______________________
Special Right Triangles. Find the remaining two sides.
30
30
6
60
2
1.
60
3.
60
2.
6 6
45
30
4.
19
45
5. What is the length of the diagonal of a square whose perimeter is 6 6 ?
6. What is the altitude of an equilateral triangle whose perimeter is 6 6 ?
7. The base angles of an isosceles trapezoid are each 60. The bases measure 10 and 18. What is
the perimeter of the trapezoid?
8. One right triangle has sides of 4 and 5. Another has sides of 3 2 and 2 5 . Which
hypotenuse is longer?
9. When you draw the diagonal of a square you make two 45-45-90 triangles.
a. What is the length of the diagonal of a square whose side is 12? _____
b. What is the length of the side of a square whose diagonal is 12 ? _____
c. What is the length of the diagonal of a square whose perimeter is 12? _______
d. What is the perimeter of a square whose diagonal is 16 2 ? ________
10. In an equilateral triangle, all angles are 60. When you draw an altitude you make two 3060-90 triangles.
30
60
a. What is the altitude of an equilateral triangle whose side is 10? ______
b. What is the side of an equilateral triangle whose altitude is 15? ______
c. What is the altitude of an equilateral triangle whose perimeter is 24? ____
d. What is the perimeter of an equilateral triangle whose altitude is 12? _____
A
B
45
60
D
C
11. In a trapezoid, when you draw the perpendiculars, you make two triangles and a rectangle.
a. If AB = 10, BD = 6 and AC = 8, how long is CD? ____________
b. If AB = 20, CD = 40 and BD = 10, how long is AC? __________
c. IF AB = BD = 8 and AC = 12, what is the perimeter of ABDC? _____
A
B
60
X
60
60
C
E
D
12. In a regular hexagon, when you draw all of the diagonals, you create six equilateral
triangles.
a. If the perimeter of the hexagon is 48, what is the height of one of the triangles?
b. If AX = 20 what is the altitude of the hexagon? ________
13. A baseball diamond is a square whose sides are all 90 ft in length.
a. How far is it from home plate to second base?
b. If the pitching rubber is exactly in the center of the diamond, how far is it from first
base?
14. If the sides of a parallelogram are 20 and 12 and the angles are 30 and 150, what is the
altitude of the parallelogram?
15. The base angles of an isosceles trapezoid are 45. The bases are 12 and 8. What is the
perimeter?
16. The base angles of an isosceles trapezoid are both 30. The bases are 12 and 8. What is the
perimeter?
17. In a rhombus, the sides are all 18 inches long. If the angles are 60, 120, 60 and 120, how
long are the diagonals?
A
B
18. A stop sign is a regular octagon. It can be divided into a square, four rectangles and four
isosceles right triangles. What is the perimeter if AB = 24?