Grade 6 Mathematics
AREA = the space INSIDE a 2D shape (measured in square units: cm^2, in^2)
SURFACE AREA = the total area of ALL faces of a 3D shape (square units)
VOLUME = the space INSIDE a 3D shape (measured in cubic units: cm^3, in^3)
Find the area of a triangle with base = 8 cm and height = 5 cm
Write the formula: A = (1/2) x b x h
Substitute the values: A = (1/2) x 8 x 5
Calculate: A = (1/2) x 40 = 20 cm^2
Why divide by 2? A triangle is exactly HALF of a rectangle with the same base and height!
Find the surface area of a box: length = 4 in, width = 3 in, height = 2 in
A rectangular prism has 6 faces (3 pairs):
- 2 faces that are l x w (top and bottom): 4 x 3 = 12 in^2 each
- 2 faces that are l x h (front and back): 4 x 2 = 8 in^2 each
- 2 faces that are w x h (left and right): 3 x 2 = 6 in^2 each
Formula: SA = 2lw + 2lh + 2wh
Calculate: SA = 2(4x3) + 2(4x2) + 2(3x2) = 2(12) + 2(8) + 2(6) = 24 + 16 + 12 = 52 in^2
Same box: length = 4 in, width = 3 in, height = 2 in
Formula: V = l x w x h
Calculate: V = 4 x 3 x 2 = 24 in^3 (cubic inches)
Think of it as: How many 1-inch cubes would fit inside the box? 24 cubes!
WRONG: Using the slanted side of a triangle or parallelogram as the height.
RIGHT: The HEIGHT must be PERPENDICULAR (at a right angle) to the base. Look for the dotted line that makes a 90-degree angle!
1. Triangle: base = 12 cm, height = 7 cm
A = (1/2) x _____ x _____ = cm^2
2. Parallelogram: base = 9 in, height = 4 in
A = _____ x _____ = in^2
3. Trapezoid: base1 = 6 m, base2 = 10 m, height = 4 m
A = (1/2)(_____ + _____) x _____ = m^2
4. Rectangular prism: length = 5 cm, width = 4 cm, height = 3 cm
Surface Area = 2(___x___) + 2(___x___) + 2(___x___) = cm^2
Volume = ___ x ___ x ___ = cm^3
5. A gift box is 8 inches long, 6 inches wide, and 3 inches tall. How much wrapping paper is needed to cover the entire box? (Find surface area)
Surface Area = in^2