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The photograph on the right shows an American Football stadium - Junior Cycle Mathematics - Question 1 - 2015
Question 1
The photograph on the right shows an American Football stadium. The pitch is outlined in white in the center of the photograph. The width of the pitch is 160 feet ... show full transcript
Worked Solution & Example Answer:The photograph on the right shows an American Football stadium - Junior Cycle Mathematics - Question 1 - 2015
Step 1
By measuring the photograph and using an appropriate scale, estimate the length of the pitch (in feet) and the area of the pitch (in square feet) as accurately as you can.
Answer
To find the area, first, we measure the width and length of the pitch in the photograph. The width (W) measures 2.1 cm and the length measures 4.8 cm. We know that the actual width of the pitch is 160 feet. Therefore, we establish a scale:
1 cm in the picture corresponds to . Thus, if we apply the scale to the length:
[\text{Actual length} = 4.8 \text{ cm} \times 76.19 \text{ ft/cm} \approx 365.714 \text{ ft}]
The area of the pitch can now be calculated:
[\text{Area} = \text{width} \times \text{length} = 160 \text{ ft} \times 365.714 \text{ ft} \approx 58,514.24 \text{ ft}^2]
Hence, the estimated area is ( 58,514.24 \text{ ft}^2 ) correct to two decimal places.
Step 2
If one metre is 3.28 feet, find the area of this pitch in square metres. Give your answer correct to the nearest whole number.
Answer
To find the area in square metres, first, we convert the measurements from feet to metres. Using the conversion factor:
[\text{Area in square metres} = \frac{\text{Area in square feet}}{(3.28)^2}]
Calculating:
[\text{Area} = \frac{58,514.24 \text{ ft}^2}{(3.28)^2} \approx \frac{58,514.24}{10.7584} \approx 5,439 \text{ m}^2]
Thus, the area is ( 5,439 \text{ m}^2 ) correct to the nearest whole number.