学习中心 / 几何

Area of common shapes and circles

Area formulas for rectangles, triangles, trapeziums and circles — and why the triangle formula has a half in it.

阅读约 1 分钟更新于 2026年10月18日作者:Sumzo team审核:Sumzo team

Area measures the space inside a flat shape, in square units (cm², m², …). Perimeter is the distance around the outside.

  • Rectangle: A=l×wA = l \times w
  • Triangle: A=12bhA = \tfrac{1}{2} b h — half of a rectangle with the same base and height
  • Parallelogram: A=bhA = b h (use the perpendicular height, not the slanted side)
  • Trapezium: A=12(a+b)hA = \tfrac{1}{2}(a + b)h

例题

Area of a triangle

A triangle has base 10 cm and height 6 cm. Find its area.

显示解题过程
  1. Use half base times height.
    A=12×10×6=30A = \tfrac{1}{2} \times 10 \times 6 = 30

答案: 30 cm²

已由 Sumzo 数学引擎核验

Circles

C=2πr,A=πr2C = 2\pi r,\qquad A = \pi r^2
r is the radius; the diameter is d = 2r.

例题

A circle of radius 5

Find the circumference and area of a circle with radius 5.

显示解题过程
  1. Circumference.
    C=2π×5=10π≈31.42C = 2\pi \times 5 = 10\pi \approx 31.42
  2. Area.
    A=π×52=25π≈78.54A = \pi \times 5^2 = 25\pi \approx 78.54

答案: Circumference 10π10\pi, area 25π25\pi

已由 Sumzo 数学引擎核验

遇到难题?问问 Sumzo AI