Question

Can anybody help me on this

Answer 1

Answer: second option

Explanation:

Find the distance AE by subtracting AB and DC and dividing by 2:

`AE=(AB-DC)/(2)\\\\AE=(15ft-7ft)/(2)\\\\AE=4ft`

Knowing the length of AD and AE, you can apply the Pythagorean Theorem to calculate the length DE:

`c=√(a^2-b^2)`

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then:

`a=AD=5ft\\b=AE=4ft\\c=DE`

Substituting values into
`c=√(a^2-b^2)` you get that the lenght of DE is:

`DE=√((5ft)^2+(4ft)^2)\\DE=3ft`

Calculate thea area of the trapezoid with the formula:

`A=(h)/(2)(B+b)`

Where h is the height, B is the larger base and b is the smaller base.

Substituting, you get:

`h=DE=3ft\\B=AB=15ft\\b=DC=7ft\\\\A=(3ft)/(2)(15ft+7ft)=33ft^2`