Question

Danielle is making a quilt with triangles and squares. There are 4 colored triangles inside each square. The base and height of each triangle is x + 4 inches as shown. Which polynomial represents the area of the colored triangles in square inches?

Answer 1

`(2x^2+16x+32)\ \text{sq. inches}`

Explanation:

b = h = Base = Height of triangle =
`(x+4)\ \text{inches}`

Area of one triangle

`A=(1)/(2)bh=(1)/(2)(x+4)(x+4)`

There are 4 colored triangles so total area of the triangles is

`4A=4* (1)/(2)(x+4)(x+4)\\\Rightarrow 4A=2(x+4)^2\\\Rightarrow 4A=2(x^2+8x+16)\\\Rightarrow 4A=2x^2+16x+32`

The area of the colored triangles is
`(2x^2+16x+32)\ \text{sq. inches}`