Question

a section of a rectangle is shaded. the area of the shaded section is 63 square units. what is the value of x? 9 units 11 units 18 units 21 units

Explanation:

Step1: Identify the shape of the shaded area

The shaded area is a trapezoid. The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, $a=x$, $b = 7$, and $h = 7$, and $A=63$.

Step2: Substitute values into the formula

Substitute the known values into the area formula: $63=\frac{(x + 7)\times7}{2}$.

Step3: Solve the equation for $x$

First, multiply both sides of the equation by 2 to get rid of the fraction: $63\times2=(x + 7)\times7$, which simplifies to $126=(x + 7)\times7$.
Then divide both sides by 7: $\frac{126}{7}=x + 7$, so $18=x + 7$.
Finally, subtract 7 from both sides: $x=18 - 7=11$.

Answer:

11 units