The figure shows 4 identical triangles inside a square. The perimeter of the square is 280 cm.

  1. (a)

    What is the length of yy?

    Ans : (a) ___ cm

  2. (b)

    The 4 triangles are then cut from the square. What is the area of the remaining figure?

    Ans : (b) ___ cm^2

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Worked solution

2(a)

1. Find the side length of the square.

Side length of square =280÷4=70 cm= 280 \div 4 = 70\text{ cm}

2. Determine the relationship between the side of the square, the vertical distance between triangles, and the length of y.

The 4 identical triangles are arranged vertically. The vertical distance between the top of one triangle and the top of the next is 20 cm20\text{ cm}.
Since there are 4 triangles, there are 3 such intervals of 20 cm20\text{ cm} from the top of the first triangle to the top of the fourth triangle.
The total vertical distance from the top of the first triangle to the top of the fourth triangle is 3×20=60 cm3 \times 20 = 60\text{ cm}.
The remaining vertical distance to the bottom of the square is the vertical leg of the bottom-most triangle, which is yy.
Therefore, the side length of the square is the sum of these distances: 60+y=7060 + y = 70.

3. Calculate the length of y.

y=70−60=10 cmy = 70 - 60 = 10\text{ cm}

Answer

1010

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