There are eight people competing in the track meet this weekend. They are competing for 1st, 2nd, and 3rd place ribbons. How man
1 answer:
You might be interested in
Check the picture below.
bear in mind that, the "bases" are the two parallel sides, and the height is the distance between them.
![\bf \textit{area of this trapezoid}\\\\ A=\cfrac{AB(BC+AD)}{2}\\\\ -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d B&({{ 3}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=\sqrt{[3-(-1)]^2+[2-5]^2}\implies AB=\sqrt{(3+1)^2+(2-5)^2} \\\\\\ AB=\sqrt{16+9}\implies AB=\sqrt{25}\implies \boxed{AB=5}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20this%20trapezoid%7D%5C%5C%5C%5C%0AA%3D%5Ccfrac%7BAB%28BC%2BAD%29%7D%7B2%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AA%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%0AB%26%28%7B%7B%203%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B%5B3-%28-1%29%5D%5E2%2B%5B2-5%5D%5E2%7D%5Cimplies%20AB%3D%5Csqrt%7B%283%2B1%29%5E2%2B%282-5%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B16%2B9%7D%5Cimplies%20AB%3D%5Csqrt%7B25%7D%5Cimplies%20%5Cboxed%7BAB%3D5%7D)
![\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d D&({{ -13}}\quad ,&{{ -11}}) \end{array} \\\\\\ AD=\sqrt{[-13-(-1)]^2+[-11-5]^2} \\\\\\ AD=\sqrt{(-13+1)^2+(-16)^2}\implies AD=\sqrt{144+256} \\\\\\ AD=\sqrt{400}\implies \boxed{AD=\sqrt{20}}](https://tex.z-dn.net/?f=%5Cbf%20-------------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AA%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%0AD%26%28%7B%7B%20-13%7D%7D%5Cquad%20%2C%26%7B%7B%20-11%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0AAD%3D%5Csqrt%7B%5B-13-%28-1%29%5D%5E2%2B%5B-11-5%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAD%3D%5Csqrt%7B%28-13%2B1%29%5E2%2B%28-16%29%5E2%7D%5Cimplies%20AD%3D%5Csqrt%7B144%2B256%7D%0A%5C%5C%5C%5C%5C%5C%0AAD%3D%5Csqrt%7B400%7D%5Cimplies%20%5Cboxed%7BAD%3D%5Csqrt%7B20%7D%7D)
so, the area for this trapezoid is then
bear in mind that, the "bases" are the two parallel sides, and the height is the distance between them.
so, the area for this trapezoid is then