Triangle — two sides and the angle between
Area and perimeter, with the formula worked through and a drawing to scale.
Result
- Area
- 15.1554 sq ft
- = 15.1554 sq ft · 1.408 m²
- Perimeter
- 18.245 ft
- = 18.245 ft · 5.5611 m
- Third side c
- 6.245 ft
The working
Area: A = ½ × a × b × sin C
Perimeter: P = a + b + c, c = √(a² + b² − 2ab cos C)
A = ½ × 7 × 5 × sin 60° = 15.1554 c = √(7² + 5² − 2 × 7 × 5 × cos 60°) = 6.245 P = 18.245
Values in feet; areas in sq ft.
About the triangle — two sides and the angle between
When you can measure two sides and the angle between them — a corner of an odd-shaped plot, say. The third side is the law of cosines.
Every formula on this site is explained step by step in Learn: area and perimeter.
Other shapes
Square Rectangle Parallelogram Rhombus Trapezoid (trapezium) Kite Triangle — three sides Triangle — base and height Right triangle Isosceles triangle Equilateral triangle Circle Semicircle Quarter circle Sector (pie slice) Circular segment (arch) Ring (annulus) Ellipse (oval) Regular polygon (pentagon, hexagon, octagon…) L-shape Any polygon — by corner points