Question

A trapezoid has vertices at A(5, 0)A(5, 0) , B(4, 3)B(4, 3) , C(10, 5)C(10, 5) , and D(8, 1)D(8, 1) , and angles A and B are right angles. What is the area of the trapezoid

Answer 1

check the picture below.





`\bf AB=√((4-5)^2+(3-0)^2)\implies AB=√(1+9)\implies AB=√(10) \\\\\\ BC=√((10-4)^2+(5-3)^2)\implies BC=√(36+4)\implies BC=√(40) \\\\\\ AD=√((8-5)^2+(1-0)^2)\implies AD=√(9+1)\implies AD=√(10)\\\\ -------------------------------`


`\bf \begin{cases} √(40)\\ \qquad √(2^2\cdot 10)\\ \qquad 2√(10) \end{cases}\qquad A=\cfrac{h(x+y)}{2}\implies A=\cfrac{√(10)(2√(10)+√(10))}{2} \\\\\\ A=\cfrac{√(10)(3√(10))}{2}\implies A=\cfrac{3(√(10))^2}{2}\implies A=\cfrac{30}{2}\implies A=15`