Question

the putting green for a hole at a miniature golf course is shown in the diagram.
20 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, here we use rectangle and trapezoid for simplicity). The rectangle has dimensions \(5\) feet (width) and \(10\) feet (height). The trapezoid has bases \(10\) feet and \(17.5\) feet, and the width (the horizontal side) is \(20 - 5=15\) feet? Wait, no, actually, another way: split into a rectangle (5ft by 17.5ft) and a triangle. Wait, let's re - examine. The vertical side is 17.5ft, the bottom horizontal is 5ft, the left part: the height difference is \(17.5 - 10 = 7.5\)ft, and the horizontal length is \(20 - 5=15\)ft? No, maybe better to split into a rectangle (5ft×10ft) and a trapezoid with bases 10ft and 17.5ft, and the length of the trapezoid's parallel side is \(20 - 5 = 15\)ft? Wait, no, let's use the correct method.

Alternative approach: The shape can be considered as a rectangle (5 ft wide and 17.5 ft tall) plus a triangle. The triangle has a base of \(20 - 5=15\)ft and a height of \(17.5 - 10 = 7.5\)ft? Wait, no, the vertical segment from the top of the 10ft side to the top of the 17.5ft side is \(17.5 - 10=7.5\)ft. The horizontal length of the triangle's base is \(20 - 5 = 15\)ft.

Wait, another way: The area of the putting green can be calculated by adding the area of a rectangle (5 ft × 17.5 ft) and the area of a trapezoid? No, let's split it into a rectangle (5ft×10ft) and a trapezoid with bases 10ft and 17.5ft, and the length of the trapezoid's non - parallel side? No, better to use the formula for the area of a composite figure.

Wait, the correct split: The figure is composed of a rectangle (width = 5ft, height = 17.5ft) and a triangle. The triangle has a base of \(20 - 5 = 15\)ft and a height of \(17.5 - 10=7.5\)ft? No, that's not right. Wait, actually, the top horizontal side is 20ft, the bottom horizontal side is 5ft. The right vertical side is 17.5ft, and the left vertical side (the shorter one) is 10ft.

So, we can calculate the area as the area of a rectangle (5ft×17.5ft) plus the area of a trapezoid with bases \(10\)ft and \(17.5\)ft? No, let's use the formula for the area of a trapezoid and a rectangle. Wait, the figure can be seen as a trapezoid (with the two parallel sides being 10ft and 17.5ft, and the distance between them is 5ft) plus a rectangle? No, I think the correct way is:

The area of the composite figure = area of rectangle (5ft×17.5ft) + area of triangle. The triangle has a base of \(20 - 5 = 15\)ft and a height of \(17.5 - 10=7.5\)ft? No, that's incorrect. Wait, the height of the triangle should be the difference in the vertical sides, which is \(17.5 - 10 = 7.5\)ft, and the base of the triangle is the difference in the horizontal sides, which is \(20 - 5=15\)ft. But the triangle is a right triangle? Wait, no, the angle at the corner where the 10ft and 15ft (20 - 5) meet is a right angle? Maybe.

Wait, let's calculate the area of the rectangle first: \(A_{rectangle}=5\times17.5 = 87.5\) square feet.

Then, the area of the triangle: The base of the triangle is \(20 - 5=15\)ft, and the height of the triangle is \(17.5 - 10 = 7.5\)ft. The area of a triangle is \(\frac{1}{2}\times base\times height=\frac{1}{2}\times15\times7.5 = 56.25\) square feet.

Then, the total area is \(87.5+56.25 = 143.75\) square feet? Wait, no, that's not correct. Wait, maybe I made a mistake in the split.

Wait, another approach: The figure can be considered as a trapezoid with the two parallel sides being 20ft and 5ft, and the height? No, the vertical sides are not parallel. Wait, let's use the formula for the area of a composite figure by subtracting? No, better to use the correct split.

Wait, the correct way is: The area of the putting green is equal to the area of a rectangle (5 ft × 17.5 ft) plus the area of a trapezoid with bases 10 ft and 17.5 ft? No, I think I messed up. Let's do it step by step.

1. Area of the rectangle: The rectangle has a width of 5 ft and a height of 17.5 ft. So, \(A_{1}=5\times17.5 = 87.5\) square feet.

2. Area of the trapezoid: The trapezoid has two parallel sides (bases) of lengths \(10\) ft and \(17.5\) ft? No, wait, the horizontal length of the trapezoid is \(20 - 5=15\) ft. The two parallel sides of the trapezoid are the vertical sides: 10 ft and 17.5 ft, and the distance between them (the horizontal length) is \(20 - 5 = 15\) ft. The formula for the area of a trapezoid is \(\frac{(a + b)}{2}\times h\), where \(a\) and \(b\) are the lengths of the parallel sides, and \(h\) is the distance between them. So, \(A_{2}=\frac{(10 + 17.5)}{2}\times15=\frac{27.5}{2}\times15 = 13.75\times15=206.25\)? No, that can't be right because the total area can't be that big.

Wait, I think I made a mistake in the split. Let's try a different split. Let's split the figure into a rectangle (5 ft × 10 ft) and a trapezoid with bases 5 ft and 20 ft, and height \(17.5 - 10 = 7.5\) ft.

Area of the rectangle: \(A_{1}=5\times10 = 50\) square feet.

Area of the trapezoid: \(\frac{(5 + 20)}{2}\times7.5=\frac{25}{2}\times7.5 = 12.5\times7.5 = 93.75\) square feet.

Total area: \(50+93.75 = 143.75\) square feet. Ah, that makes sense.

Let's verify:

The rectangle is 5ft wide and 10ft tall: area = 5×10 = 50.

The trapezoid has bases of 5ft (the bottom side) and 20ft (the top side), and the height is the difference in the vertical sides, which is \(17.5 - 10 = 7.5\)ft. The formula for the area of a trapezoid is \(\frac{(base1 + base2)}{2}\times height\). So, \(\frac{(5 + 20)}{2}\times7.5=\frac{25}{2}\times7.5 = 12.5\times7.5 = 93.75\).

Adding the two areas: \(50+93.75 = 143.75\) square feet.

Step2: Calculate the area of the rectangle

The rectangle has a width \(w = 5\) ft and a height \(h = 10\) ft. The area of a rectangle is given by \(A_{rectangle}=w\times h\). So, \(A_{rectangle}=5\times10 = 50\) square feet.

Step3: Calculate the area of the trapezoid

The trapezoid has two parallel sides (bases) \(b_1 = 5\) ft and \(b_2 = 20\) ft, and the height \(h_{trapezoid}=17.5 - 10 = 7.5\) ft. The area of a trapezoid is given by \(A_{trapezoid}=\frac{(b_1 + b_2)}{2}\times h_{trapezoid}\).

Substitute the values: \(\frac{(5 + 20)}{2}\times7.5=\frac{25}{2}\times7.5 = 12.5\times7.5 = 93.75\) square feet.

Step4: Calculate the total area

The total area of the putting green is the sum of the area of the rectangle and the area of the trapezoid. So, \(A_{total}=A_{rectangle}+A_{trapezoid}=50 + 93.75=143.75\) square feet.

Answer:

\(143.75\)