Trapezoid - hard example

Base of the trapezoid are: 24, 16 cm.
Diagonal 22, 26 cm.
Calculate its area and perimeter.

Correct result:

S = 264 cm²
o = 67.9663 cm

Solution:

a = 24 cm c = 16 cm u = 22 cm v = 26 cm w = a + c = 24 + 16 = 40 cm s = \frac{u + v + w}{2} = \frac{22 + 26 + 40}{2} = 44 cm S = \sqrt{s \cdot (s - w) \cdot (s - u) \cdot (s - v)} = \sqrt{44 \cdot (44 - 40) \cdot (44 - 22) \cdot (44 - 26)} = 264 {cm}^{2}

Try calculation via our triangle calculator.

S = \frac{a + c}{2} \cdot h = \frac{w}{2} \cdot h h = 2 \cdot S / w = 2 \cdot 264 / 40 = \frac{66}{5} = 13.2 cm u^{2} = h^{2} + a_{1}^{2} = 13. 2^{2} + 17. 6^{2} = \frac{4356}{25} = 174.24 a_{1} = \sqrt{u^{2} - h^{2}} = \sqrt{2 2^{2} - 13. 2^{2}} = \frac{88}{5} = 17.6 cm a_{2} = a - a_{1} = 24 - 17.6 = \frac{32}{5} = 6.4 cm b^{2} = h^{2} + a_{2}^{2} b = \sqrt{h^{2} + a_{2}^{2}} = \sqrt{13. 2^{2} + 6. 4^{2}} ≐ 14.6697 cm c_{1} = \sqrt{v^{2} - h^{2}} = \sqrt{2 6^{2} - 13. 2^{2}} = \frac{112}{5} = 22.4 cm c_{2} = a - c_{1} = 24 - 22.4 = \frac{8}{5} = 1.6 cm d^{2} = h^{2} + c_{2}^{2} d = \sqrt{h^{2} + c_{2}^{2}} = \sqrt{13. 2^{2} + 1. 6^{2}} ≐ 13.2966 cm o = a + b + c + d = 24 + 14.6697 + 16 + 13.2966 = 67.9663 cm

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