Geometry
Area and Volume flashcards
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- What is the area formula for a triangle?Area of Polygons
- A = ½bh, where h is the perpendicular height to base b.
- What is the area formula for a parallelogram?Area of Polygons
- A = bh, using the perpendicular height, not the slanted side.
- What is the area formula for a trapezoid?Area of Polygons
- A = ½(b₁ + b₂)h: average the parallel bases, then multiply by the height.
- How do you find the area of a composite figure by adding?Area of Composite Figures
- Split a shape into pieces that do not overlap. Find each piece’s area, then add them.
- When do you subtract to find the area of a composite figure?Area of Composite Figures
- When a piece is cut out: find the area of the whole shape, then subtract the missing piece.
- How many square centimeters are in one square meter?Area of Composite Figures
- 10,000 cm², because 1 m = 100 cm and 100 × 100 = 10,000.
- How do you find the surface area of a prism?Surface Area of Solids
- Add the areas of the two bases and all the lateral faces.
- How do you find the surface area of a cylinder?Surface Area of Solids
- Add the two circular bases and the lateral area: 2πr² + 2πrh.
- How can a net help find surface area?Surface Area of Solids
- Unfold a solid into a flat net, find the area of each face, and add them.
- What is the volume formula for a prism?Volume of Prisms and Cylinders
- V = Bh: base area times height.
- What is the volume formula for a cylinder?Volume of Prisms and Cylinders
- V = πr²h.
- If every dimension of a solid is doubled, how does its volume change?Volume of Prisms and Cylinders
- It becomes 8 times as large, because 2 × 2 × 2 = 8.
- What is the volume formula for a pyramid?Pyramids, Cones, and Spheres
- V = ⅓Bh, one third of a prism with the same base and height.
- What is the volume formula for a cone?Pyramids, Cones, and Spheres
- V = ⅓πr²h, one third of a cylinder with the same radius and height.
- What is the volume formula for a sphere?Pyramids, Cones, and Spheres
- V = (4/3)πr³.