Area of parallelogram

Question

In a garden of the shape of an isosceles right triangle is shown as ABC. The length of the longest side of the garden is 120√2 m. D and E are the mid-points of AB and BC respectively. A pond is to be dug in the portion marked by ?DBE and the remaining part is to be covered with green grass. If the rates of digging the pond and covering by grass are $1080 per m² and $600 per m². Find the total cost of the above two jobs.

Answer 1

An isosceles right triangle is a right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of 45º, 45º, and 90º. For an isosceles right triangle with side lengths a, the hypotenuse has length a√2, and the area is a2/2 
    ---- http://mathworld.wolfram.com/IsoscelesRightTriangle.html
 
The triangle described in the problem has two sides of length a=120.  D and E are assumed to be midpoints of those sides.
 
This makes two isosceles right triangles and a parallelogram:
    original one:  a=120,  A = 1202/2=7200 m2
     pond:         a=60,   A=602/2=1800 m2
 
Total cost of project = cost of digging pond + cost of planting grass
     Total cost   =  (1080)(1800)        +   (600)(7200-1800)
     Total cost   =  $ 5184000
 
Now, I realize that this is a math problem, but I would advise checking the units and costs.  Also, be careful with decimal points if they are changed.