Question

the putting green for a hole at a miniature golf course is shown in the diagram.
15 feet
15 feet
7.5 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 \(15\) feet (height)? Wait, no, let's look again. Alternatively, split into a rectangle (bottom part) and a trapezoid (top part). The bottom rectangle: width \(5\) ft, height \(15 - 7.5=7.5\) ft? Wait, maybe better to split into a rectangle (5ft by 15ft? No, the vertical side is 15ft, the horizontal top is 15ft, the bottom horizontal is 5ft, and the vertical middle is 7.5ft. Wait, another approach: the shape can be considered as a combination of a rectangle (5ft by 15ft) and a trapezoid with bases \(15 - 5 = 10\) ft and \(15\) ft? No, maybe split into a triangle and a rectangle. Wait, let's calculate the area by adding a rectangle and a trapezoid. Wait, the total height is 15ft, the lower part is a rectangle with width 5ft and height 15ft? No, the white part is a rectangle? Wait, no, the green shape: let's split it into two parts: a rectangle (5ft by 15ft) and a trapezoid with bases \(15\) ft and \(15 - 5 = 10\) ft? No, maybe the correct way is: the green area can be calculated as the area of a rectangle (5ft by 15ft) plus the area of a trapezoid with bases \(15 - 5 = 10\) ft and \(15\) ft? Wait, no, let's use coordinates. Alternatively, the area can be found by adding the area of a rectangle (5ft by 15ft) and the area of a triangle? Wait, no, let's look at the dimensions. The top horizontal side is 15ft, the right vertical side is 15ft, the bottom horizontal side is 5ft, and the middle vertical side is 7.5ft. So, the green shape can be divided into a rectangle (5ft by 15ft) and a trapezoid with bases \(15 - 5 = 10\) ft and \(15\) ft? No, the height of the trapezoid would be \(15 - 7.5 = 7.5\) ft? Wait, maybe another way: the area is the area of a square (15ft by 15ft) minus the area of the white rectangle? No, the white part is a rectangle? Wait, the white part has width \(15 - 5 = 10\) ft and height \(7.5\) ft? Wait, no, the white part is a rectangle with width \(15 - 5 = 10\) ft and height \(7.5\) ft? Then the green area would be the area of the big square (15x15) minus the area of the white rectangle (10x7.5). Wait, 15x15=225, 10x7.5=75, 225-75=150? No, that can't be. Wait, no, the big square is 15x15, but the top left is a triangle? Wait, no, the diagram: the green shape has a top horizontal side of 15ft, right vertical side of 15ft, bottom horizontal side of 5ft, and a vertical side at 7.5ft from the bottom. So, the green area can be calculated as the area of a rectangle (5ft by 15ft) plus the area of a trapezoid with bases \(15\) ft and \(15 - 5 = 10\) ft? No, the height of the trapezoid is \(15 - 7.5 = 7.5\) ft. Wait, trapezoid area formula is \(\frac{(a + b)}{2} \times h\), where \(a\) and \(b\) are the two parallel sides. So, the trapezoid has \(a = 15\) ft, \(b = 15 - 5 = 10\) ft? No, wait, the horizontal sides: the top is 15ft, the bottom of the trapezoid is \(15 - 5 = 10\) ft? No, the bottom of the trapezoid is 15ft? Wait, I think I'm overcomplicating. Let's use the correct method: split the green shape into a rectangle (5ft by 15ft) and a trapezoid with bases \(15\) ft and \(15 - 5 = 10\) ft? No, the height of the trapezoid is \(15 - 7.5 = 7.5\) ft. Wait, no, the vertical length from the 7.5ft mark to the top is \(15 - 7.5 = 7.5\) ft. So the trapezoid has bases \(15\) ft (top) and \(5\) ft (bottom of the trapezoid? No, the bottom of the trapezoid is 5ft? Wait, no, the green shape's bottom is 5ft, and the middle vertical line is 7.5ft. So, the green area is a rectangle (5ft by 15ft) plus a trapezoid with bases \(15 - 5 = 10\) ft and \(15\) ft? No, the height of the trapezoid is \(7.5\) ft. Wait, let's calculate:

First, the rectangle: width 5ft, height 15ft? No, the height of the rectangle is 15ft? No, the vertical side is 15ft, but the middle vertical line is 7.5ft, so the lower part is a rectangle with width 5ft and height 15ft? No, that would include the white part. Wait, no, the white part is a rectangle with width \(15 - 5 = 10\) ft and height \(7.5\) ft. So the total area of the square (15x15) is 225. Subtract the white rectangle: 10x7.5=75. So 225-75=150? But that seems off. Wait, another approach: the green shape can be divided into a rectangle (5ft by 15ft) and a triangle? No, the top part is a trapezoid. Wait, let's use the formula for the area of a composite shape. The green area is equal to the area of a rectangle (5ft by 15ft) plus the area of a trapezoid with bases \(15\) ft and \(15 - 5 = 10\) ft, and height \(15 - 7.5 = 7.5\) ft. Wait, trapezoid area: \(\frac{(15 + 10)}{2} \times 7.5 = \frac{25}{2} \times 7.5 = 12.5 \times 7.5 = 93.75\). Rectangle area: 5x15=75. Total: 93.75+75=168.75? No, that's not right. Wait, maybe the correct split is a rectangle (5ft by 7.5ft) and a trapezoid with bases 15ft and 5ft, height 7.5ft? Wait, no, the height of the trapezoid would be 15 - 7.5 = 7.5ft. Wait, let's look at the diagram again. The green shape: the right side is 15ft, the bottom is 5ft, the top is 15ft, and there's a vertical line at 7.5ft from the bottom. So, the area can be calculated as the area of a rectangle (5ft by 15ft) plus the area of a triangle with base \(15 - 5 = 10\) ft and height \(15 - 7.5 = 7.5\) ft? Wait, triangle area: \(\frac{1}{2} \times 10 \times 7.5 = 37.5\). Rectangle area: 5x15=75. Total: 75+37.5=112.5? No, that's not. Wait, maybe I'm misinterpreting the diagram. Let's try another way: the shape is a combination of a rectangle (5ft by 15ft) and a trapezoid with bases 15ft and 5ft, and height (15 - 7.5)=7.5ft. Wait, trapezoid area: \(\frac{(15 + 5)}{2} \times 7.5 = \frac{20}{2} \times 7.5 = 10 \times 7.5 = 75\). Rectangle area: 5x7.5=37.5? No, the height of the rectangle would be 7.5ft? Wait, the vertical side is 15ft, with a 7.5ft segment. So the lower rectangle is 5ft by 7.5ft, and the upper trapezoid has bases 15ft and 5ft, height 7.5ft. Then total area: 5x7.5 + \(\frac{(15 + 5)}{2} \times 7.5\) = 37.5 + 75 = 112.5? No, that's not. Wait, maybe the correct answer is 112.5? Wait, no, let's calculate again. Wait, the diagram: the top horizontal is 15ft, right vertical 15ft, bottom horizontal 5ft, middle vertical 7.5ft. So the green area can be seen as a rectangle (5ft by 15ft) minus a smaller rectangle (10ft by 7.5ft)? No, 15x5=75, 10x7.5=75, 75+75=150? Wait, no, that would be if we add. Wait, maybe the shape is a square (15x15) minus a rectangle (10x7.5). 15x15=225, 10x7.5=75, 225-75=150. But that doesn't seem right. Wait, maybe I made a mistake. Let's use the formula for the area of a trapezoid and a rectangle. Wait, the green shape can be divided into a rectangle (5ft by 15ft) and a trapezoid with bases (15-5)=10ft and 15ft, height (15-7.5)=7.5ft. Wait, trapezoid area: (10+15)/2 *7.5=25/2*7.5=12.5*7.5=93.75. Rectangle area:5*15=75. Total:93.75+75=168.75. No, that's too big. Wait, maybe the middle vertical line is 7.5ft, so the height of the trapezoid is 7.5ft, and the bases are 15ft and 5ft. Then trapezoid area: (15+5)/2 *7.5=10*7.5=75. Rectangle area:5*7.5=37.5. Total:75+37.5=112.5. Yes, that makes sense. So the area is 112.5 square feet.

Wait, let's verify: the lower part is a rectangle 5ft by 7.5ft (area 37.5), the upper part is a trapezoid with bases 15ft and 5ft, height 7.5ft (area (15+5)/2 *7.5=75). So total 37.5+75=112.5. So the area is 112.5 square feet.

Step2: Calculate the area

First, identify the two parts: a rectangle (5 ft by 7.5 ft) and a trapezoid (bases 15 ft and 5 ft, height 7.5 ft).

- Area of rectangle: \( A_{rectangle} = \text{width} \times \text{height} = 5 \times 7.5 = 37.5 \) square feet.
- Area of trapezoid: \( A_{trapezoid} = \frac{(b_1 + b_2)}{2} \times h = \frac{(15 + 5)}{2} \times 7.5 = 10 \times 7.5 = 75 \) square feet.

Total area: \( 37.5 + 75 = 112.5 \) square feet.

Answer:

112.5