Angle Relationships
Two angles are supplementary.
One angle = 128°
Find the other angle.
180−128=52°
A circle has radius 4 cm.
Find the circumference.
C= 25.12
Cylinder:
r = 3
h = 5
Find volume.
141.3
L-Shape
Rectangles 6×4 and 4×3
→ Area?
24 + 12 = 36
Circle Area
r=9 → Area?
254.47
Angles x and 68° are complementary.
Find x
x=22
A circle has diameter 14 inches.
Find the radius.
7 inches
Rectangular Prism
l=5
w=3
h=4 → Volume?
60 cm³ (5 × 3 × 4)
Rectangle + Semicircle
Rectangle 10×5
semicircle r=5
→ Area?
Rectangle = 50
Semicircle = (1/2)π×25 = 12.5π
→ Total = 50 + 12.5π
=89.25
Cylinder Volume
r=7
h=8
→ Volume?
1230.89
Two vertical angles are shown.
One angle = (3x + 12)
The other = (5x − 6)
Find x
3x + 12 = 5x − 6
2x = 18
x = 9
Radius = 5 cm
Find area.
A= 78.5
Cube
Side = 6
Volume?
216 cm³ (6³)
Triangle + Rectangle
Triangle b=6 h=4
rectangle 6×3
→ Total area?
Triangle = 12
Rectangle = 18
→ Total = 30
Rectangular Prism Volume
l=5
w=6
h=4 →
5×6×4 = 120
Two angles form a linear pair.
One angle is (4x − 10)
The other is (2x + 40)
Find x
4x − 10 + 2x + 40 = 180
6x + 30 = 180
x = 25
Rectangle 12 × 8 cm. Area?
96 cm²
Pyramid (Square Base)
Base 9 × 9
height 12
Volume?
324 cm³ (V = 1/3 × 81 × 12 = 324)
Square – Circle
Square 12×12
circle r=4 removed
→ Remaining area?
Square = 144
Circle = 16π
→ Remaining = 144 – 16π
= 93.76
Circumference of a circle.
R= 12
75.4
Two complementary angles are (x + 12) and (2x − 6).
Find x
x + 12 + 2x − 6 = 90
3x + 6 = 90
x = 28
Rectangle 12 × 6 m + semicircle radius 6 m. Total area?
Rectangle = 72, Semicircle = (1/2)πr² = 18π → Total = 72 + 18π m² or 128.52 m²
Composite 3D
Cylinder r=3 h=8
Rectangular prism 4×5×6
→ Total Volume?
Cylinder: π×9×8 = 72π, Prism: 4×5×6 = 120 → Total = 72π + 120 OR 346.08
Complex Composite
Rectangle 10×6
triangle b=6 h=4
semicircle r=3
→ Total area?
Rectangle = 60
Triangle = 12
Semicircle = 14.14
→ Total ≈ 86.14
A triangular prism has a triangular base with
a base of 5
a height of 2
and a prism length of 10
What is its volume?