Question 231154
Hello, 

We can find the area of triangle DEF by using the hypotenuse Formula. 

                     DF(squared) + EF(squared)= DE(squared) 

Plug in the numbers. 

                      DF(squared) + 7(squared) = 12(squared)

Do the math. 

                      DF(sq)+ 49 = 144

Subtract 49 from both sides. 

                      DF (sq) = 95

Square root both sides. 

                       DF = sq root of 95
Now plug in the area formula for that triangle which is 1/2 Base times height

                       1/2(7)sq rt 95 or 
   
                          3.5 sq rt 95  we can approx sq rt of 95 to 9.75 

Therefore:               area of this triangle is 34.125 Sq Units

Now plug in the area formula for triangle DFG. 

                     1/2(9.75)10 = Area

Do the math. 

                      48.75 Square Units

Add both triangles and you have: 

                       82.875 square units

RJ Toftness
Author "Unlock the Mystery to Math"
www.math-unlock.com