Find an expression

• Dec 2nd 2013, 09:43 AM
Bhoona
Find an expression
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?
• Dec 2nd 2013, 12:04 PM
topsquark
Re: Find an expression
Quote:

Originally Posted by Bhoona
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?

Area of kite: (1/2)(x - 4)(x - 4)
Area of triangle (1/2)(x - 2)(x - 4)

Now subtract.

-Dan
• Dec 2nd 2013, 12:50 PM
Bhoona
Re: Find an expression
Ok thank you.
• Dec 2nd 2013, 01:04 PM
HallsofIvy
Re: Find an expression
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.