Topic A: Flat Shapes
Perimeter, area, circles, and right triangles.
01 — Perimeter & Area
Perimeter & Area
Perimeter is the distance around a shape. Area is the space inside it.
- Rectangle: P = 2l + 2w, A = l × w.
- Triangle: A = ½ × b × h.
- Parallelogram: A = b × h. Trapezoid: A = ½ × h × (b₁ + b₂).
- Units: perimeter is in units (ft), area is in square units (ft²).
Example: A room is 12 ft by 10 ft. Area = 120 ft². Perimeter = 44 ft.
Practice — Perimeter & Area
Q1 · Short Answer
A triangle has base 10 and height 6. What is its area?
Q2 · Multiple Choice
A rectangle is 8 m long and 5 m wide. What is its perimeter?
02 — Circles & Right Triangles
Circles & the Pythagorean Theorem
Circles use π (about 3.14). Right triangles use a² + b² = c².
- Circumference: C = 2πr or C = πd.
- Area of a circle: A = πr².
- Radius vs diameter: the diameter is twice the radius.
- Pythagorean theorem: a² + b² = c², where c is the long side across from the right angle.
Example: Legs 6 and 8: 36 + 64 = 100, so c = √100 = 10.
Practice — Circles & the Pythagorean Theorem
Q3 · Short Answer
A right triangle has legs 5 and 12. How long is the hypotenuse?
Q4 · Multiple Choice
A circle has a diameter of 10. What is its area? (use π ≈ 3.14)
Topic B: Solid Shapes
Volume and surface area of 3D figures.
03 — Volume
Volume of Solids
Volume is how much a 3D shape can hold. It's measured in cubic units (ft³).
- Rectangular prism (box): V = l × w × h.
- Cylinder: V = πr²h.
- Cone: V = ⅓πr²h. Pyramid: V = ⅓ × base area × h.
- Sphere: V = ⁴⁄₃πr³.
Example: A box 4 × 3 × 2 holds 24 cubic units.
Practice — Volume of Solids
Q5 · Short Answer
What is the volume of a box that is 5 cm by 4 cm by 3 cm? (just the number)
Q6 · Multiple Choice
A cylinder has radius 2 and height 5. What is its volume? (use π ≈ 3.14)
04 — Surface Area
Surface Area
Surface area is the total area of all the outside faces, like the wrapping paper for a gift.
- Rectangular prism: SA = 2lw + 2lh + 2wh.
- Cube: SA = 6s².
- Cylinder: SA = 2πrh + 2πr².
- Tip: volume = filling it up; surface area = covering it.
Example: A cube with sides 3: SA = 6 × 9 = 54 square units.
Practice — Surface Area
Q7 · Short Answer
What is the surface area of a cube with side length 4?
Q8 · Multiple Choice
You want to paint the outside of a box. Which do you need?