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

Answer:

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

Step-by-step explanation:

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

Area of one triangle

$A=\dfrac{1}{2}bh=\dfrac{1}{2}(x+4)(x+4)$

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

$4A=4\times \dfrac{1}{2}(x+4)(x+4)\\\Rightarrow 4A=2(x+4)^2\\\Rightarrow 4A=2(x^2+8x+16)\\\Rightarrow 4A=2x^2+16x+32$

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