Question

write a quadratic function for the area of the figure. then, find the area for the given value of x.
x = 4.2
a(x) = \square (simplify your answer.)

Explanation:

Step1: Recall area formula for triangle

The figure is a right triangle with legs of length \( x \). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). Here, base \( = x \) and height \( = x \).
So, \( A(x)=\frac{1}{2}\times x\times x=\frac{1}{2}x^{2} \)

Step2: Find area when \( x = 4.2 \)

Substitute \( x = 4.2 \) into \( A(x)=\frac{1}{2}x^{2} \).
First, calculate \( x^{2}=(4.2)^{2}=17.64 \)
Then, \( A(4.2)=\frac{1}{2}\times17.64 = 8.82 \)

Answer:

For the quadratic function: \( A(x)=\frac{1}{2}x^{2} \)
For \( x = 4.2 \), the area is \( 8.82 \)