Question

Part A- A playground has the shape of a trapezoid. The shortest side of the playground and it’s width have the same dimension. Write numbers in the boxes below to show the missing dimensions in the figure above. Part B- use the measurements from part a to find the area of the playground.

Answer 1

Part A. For part A we need to identify the shorter base and the longer base of the trapezoid.

We are indicated that the shortest side and the width of the trapezoid are equal. In the following diagram we can see the width of the trapezoid:

And since the with is equal to the shortest base:

`\text{Shortest }base\text{ = 6yd}`

We still need to find the longer base. For this, we consider the dimensions that we know so far:

We have the shorter base represented in green, and lengths of 1 yd at each side of the trapezoid represented in yellow. The longer base will be the sum of the red and green lengths:

`\begin{gathered} \text{longer side = 1 yd+ 6yd + 1yd} \\ \text{longer side= 8yd} \end{gathered}`

The length of the longer side is 8yd.

Part B.

To find the area of the trapezoid, we use the following formula:

`A=(h(a+b))/(2)`

Where h is the height of the trapezoid, a is the short base and b is the long base. In this case, the height is the width:

`\begin{gathered} h=6yd \\ a=6yd \\ b=8yd \end{gathered}`

Substituting these values into the formula:

`A=((6yd)(6yd+8yd))/(2)`

Solving the operations to find the area:

`\begin{gathered} A=((6yd)(14yd))/(2) \\ A=(84yd^2)/(2) \\ A=42yd^2 \end{gathered}`

The area is

`42yd^2`