Question

Find the area of the trapezoid.
Answer option: 64ft, 48sqrt3, 32sqrt3, 54sqrt3

Answer 1

Answer: OPTION 2

Explanation:

1. Calculate the missing leg of the right triangle shown in the figure, with Pythagorean Theorem:

`x=\sqrt{(8ft)^(2)-(4√(3)ft)^(2)}=4ft`

3. The area of the triangle is:

`A=(4ft*4√(3)ft)/(2)=8√(3)ft^2`

4. The area of the rectangle is:

`A=10*4√(3)=40√(3)ft^(2)`

5. The total area is:

`A_t=40√(3)+8√(3)=48√(3)ft^(2)`

Answer 2

ANSWER


`Area=32 √(3) \: \: {ft}^(2)`


EXPLANATION

The area of a tra-pezoid is given by



`Area= (1)/(2) (sum \:of \: parallel \: sides) * height`

Let the base of the triangular portion be x.


From Pythagoras Theorem,


`{x}^(2) + {(4 √(3))}^(2) = {8}^(2)`





`{x}^(2) + 48 = 64`





`{x}^(2)=64 - 48`




`{x}^(2)=16`



`x = √(16)`


`x = 4 \: ft`


This implies that the shorter parallel side of the tra-pezoid


`= 10 - 4=6 \: ft`


We now substitute into the formula to obtain,



`Area= (1)/(2) (10 + 6) * 4 √(3) \: \: {ft}^(2)`



`Area= (1)/(2) (16) * 4 √(3) \: \: {ft}^(2)`



`Area=32 √(3) \: \: {ft}^(2)`