The area of a kite is found by multiplying the length of the diagonals together and then halving the answer.
Kite d1=x-4, d2= x-4
triangle height = x-2, base = x-4
Find an expression for the difference in areas of two shapes
the answer is x-4 but i don't understand why?
Personally, I dislike saying "the difference in areas is x- 4". In fact, I was ready to say "that can't be right, it has the wrong units- "x- 4" is a distance and would be measured in meters, feet, etc. while the areas and difference in areas would be in "square meters", "square feet", etc.
If distances are measured in meters, the area of the kite is (1/2)(x- 4 meters)(x- 4 meters)= (1/2)(x- 4)(x- 4) square meters. The area of the triangle is (1/2)(x- 2 meters)(x- 4 meters)= (1/2)(x- 2)(x- 4) square meters. The difference is (1/2)(x- 2)(x- 4)- (1/2)(x- 4)(x- 4) square meters. We can factor out 1/2 and x- 4 to get (1/2)(x- 4 meters)(x- 2- (x- 4) meters)= (1/2)(x- 4 meters)(2 meters) square meters= x- 4 square meters.