Refer to the picture attached
We let the slant height be x.
This would make the shorter base be x and the longer base be 1 1/2 x
In order to know the value of x we would need to perform the Pythagorean Theorem which is
[tex]a^2+b^2=c^2[/tex]
[tex]( \frac{x}{4} )^2+100^2=x^2 \\ \frac{x^2}{16} +10000=x^2 \\ x^2+10000=16x^2 \\ 10000=15x^2 \\ \sqrt{\frac{10000}{15}} = \sqrt{x^2} \\ \frac{100}{ \sqrt{15} } =x \\ \frac{100 \sqrt{15} }{15} =x \\ \frac{20 \sqrt{15} }{3} =x[/tex]
The area of a trapezoid is:
[tex]Area= \frac{(b_1+b_2)h}{2} = \frac{( \frac{20 \sqrt{15} }{3} +10 \sqrt{15})100 }{2} = ( \frac{50 \sqrt{15} }{3} )*50= \frac{2500 \sqrt{15} }{3}cm^2 [/tex]
