Base/Area/Height of a rectangle

Question

1. The base of a rectangle is 2X + 4, and the height is X + 4. What is the area of the rectangle?

 

2. Now, find the area of the rectangle in #1 if X equals 10?

 

then, the area of the rectangle is X(to the second power) + 3X + 1. What is the sum of the area of the two rectangles in # 1 and 2?

Answer 1

The area of a rectangle = Base X Height. So, for #1, you are not going to find a numerical answer, rather, you are going to find a formula. You just multiply 2x + 4 by x + 4.

(2x + 4)(x + 4) = 2x^2 + 8x + 4x + 16 = 2x^2 + 12x + 16

 

If x = 10, just plug 10 in for x in the formula we got: 2(10^2) + 12(10) + 16 = 200 + 120 +16 = 336.

 

For the third part, we just add the two formulas:2x^2 + 12x + 16 + x^2 + 3X + 1 = 3x^2 + 15x + 17

 

Hope that helps.

 

Steve