Question

robert built a table that has a top in the shape of a hexagon as shown. what is the area, in square feet, of the top of roberts table? a) 26 square feet b) 52 square feet c) 61 square feet d) 64 square feet

Explanation:

Step1: Divide the hexagon into rectangles and triangles

We can divide the given hexagon into two congruent trapezoids. 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.

Step2: Identify the values for the trapezoid

For each trapezoid, $a = 5$ feet, $b = 8$ feet, and $h = 4$ feet.

Step3: Calculate the area of one trapezoid

Using the formula $A=\frac{(a + b)h}{2}$, we substitute $a = 5$, $b = 8$, and $h = 4$. So $A_1=\frac{(5 + 8)\times4}{2}=\frac{13\times4}{2}=26$ square feet.

Step4: Calculate the area of the hexagon

Since the hexagon is composed of two congruent trapezoids, the area of the hexagon $A = 2\times A_1$. Substituting $A_1 = 26$ square feet, we get $A=2\times26 = 52$ square feet.

Answer:

B. 52 square feet