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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

( \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

The area of a trapezoid is:
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
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