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The diagram consists of three mathematically similar shapes - OCR - GCSE Maths - Question 17 - 2018 - Paper 5
Question 17
The diagram consists of three mathematically similar shapes. The heights of the shapes are in the ratio 1 : 4 : 5. Find the ratio total shaded area : total unshade... show full transcript
Worked Solution & Example Answer:The diagram consists of three mathematically similar shapes - OCR - GCSE Maths - Question 17 - 2018 - Paper 5
Step 1
total shaded area
Answer
Let the heights of the shapes be represented as 1h, 4h, and 5h respectively.
The area of similar shapes relates to the square of their heights. Therefore:
- The area of the first shape is proportional to \((1h)^2 = 1h^2).
- The area of the second shape is proportional to \((4h)^2 = 16h^2).
- The area of the third shape is proportional to \((5h)^2 = 25h^2).
Thus, the total area of all three shapes is:
Step 2
Step 3