Question

the putting green for a hole at a miniature golf course is shown in the diagram.
15 feet
17.5 feet
10 feet
5 feet
what is the area of the putting green?
□ feet²

Explanation:

Step1: Split the shape

We can split the putting green into a rectangle and a trapezoid (or a triangle and a rectangle, but let's use rectangle and trapezoid for clarity). The rectangle has dimensions \( 5 \) feet (width) and \( 10 \) feet (height). The remaining part is a trapezoid with bases \( 5 \) feet and \( 15 \) feet, and height \( 17.5 - 10 = 7.5 \) feet.

Step2: Calculate area of rectangle

The area of a rectangle is \( \text{length} \times \text{width} \). So for the rectangle, \( A_{rectangle} = 5 \times 10 = 50 \) square feet.

Step3: Calculate area of trapezoid

The formula for the area of a trapezoid is \( \frac{(a + b)}{2} \times h \), where \( a \) and \( b \) are the bases, and \( h \) is the height. Here, \( a = 5 \), \( b = 15 \), \( h = 7.5 \). So \( A_{trapezoid} = \frac{(5 + 15)}{2} \times 7.5 = \frac{20}{2} \times 7.5 = 10 \times 7.5 = 75 \) square feet.

Step4: Total area

Add the area of the rectangle and the trapezoid: \( A_{total} = 50 + 75 = 125 \) square feet. (Alternatively, another way: split into a rectangle \( 5\times17.5 \) and a triangle with base \( 15 - 5 = 10 \) and height \( 17.5 - 10 = 7.5 \). Area of rectangle: \( 5\times17.5 = 87.5 \), area of triangle: \( \frac{1}{2} \times 10 \times 7.5 = 37.5 \), total \( 87.5 + 37.5 = 125 \))

Answer:

\( 125 \)