Triangle — three sides
Area and perimeter, with the formula worked through and a drawing to scale.
Result
- Area
- 14.6969 sq ft
- = 14.6969 sq ft · 1.3654 m²
- Perimeter
- 18 ft
- = 18 ft · 5.4864 m
- Height on side a
- 5.8788 ft
- A (opposite a)
- 44.4153°
- B (opposite b)
- 57.1217°
- C (opposite c)
- 78.463°
The working
Area: A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
Perimeter: P = a + b + c
s = (5 + 6 + 7) ÷ 2 = 9 A = √(9 × 4 × 3 × 2) = 14.6969 P = 18
Values in feet; areas in sq ft.
About the triangle — three sides
Heron's formula: with three sides you need no angles and no height. The sides must pass the triangle test — any two together longer than the third.
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 — base and height Right triangle Isosceles triangle Equilateral triangle Triangle — two sides and the angle between 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