Circle Radius Diameter B737Eb

1. **Problem Statement:** We are given a stepped polygon with vertical steps of lengths $2cm$, $4cm$, and $2cm$, and a bottom horizontal length of $15cm$. 2. **(i) Write two radii:** The term "අරය 2ක් ලියන්න" means to write two radii. For a circle, the radius is the distance from the center to any point on the circle. Here, the radii are given as $3cm$ and $5cm$ in parts (b) and (ii). 3. **(ii) Write the diameter:** The diameter is twice the radius. If the radius is $r$, then diameter $d = 2r$. 4. **(b) If the radius of the circle is $3cm$, find the diameter:** Using the formula: $$d = 2r$$ Substitute $r = 3cm$: $$d = 2 \times 3 = 6cm$$ 5. **(ii) Draw a circle with radius $5cm$:** A circle with radius $5cm$ means all points are $5cm$ from the center. 6. **(iii) Find the area of the figure:** The figure is a stepped polygon composed of three rectangles stacked vertically: - Left vertical step height: $2cm$ - Middle vertical step height: $4cm$ - Right vertical step height: $2cm$ - Bottom horizontal length: $15cm$ We can split the figure into three rectangles: - Rectangle 1 (left step): width $2cm$, height $2cm$ - Rectangle 2 (middle step): width $4cm$, height $4cm$ - Rectangle 3 (right step): width $2cm$, height $2cm$ Total width is $2 + 4 + 2 = 8cm$, but the bottom length is $15cm$, so the bottom rectangle extends beyond the steps. Let's consider the bottom rectangle as $15cm$ width and height $2cm$ (lowest step height). Area of bottom rectangle: $$A_1 = 15 \times 2 = 30cm^2$$ Area of middle step (above bottom): Height difference between middle and bottom step is $4cm - 2cm = 2cm$ Width of middle step is $4cm$ $$A_2 = 4 \times 2 = 8cm^2$$ Area of left step (above bottom): Height difference between left and bottom step is $2cm - 2cm = 0cm$ (same height), so no extra area. Area of right step (above bottom): Height difference between right and bottom step is $2cm - 2cm = 0cm$ (same height), so no extra area. Total area: $$A = A_1 + A_2 = 30 + 8 = 38cm^2$$ So, the area of the figure is $38cm^2$.