1. Draw the example compound pool: a rectangle 6.00 m by 4.00 m with a right-angled triangle attached externally along 3.00 m of the 6.00 m side. Label all sides and angles. (Use the box below.)

2. The triangle attached is a right triangle with legs 3.00 m and 4.00 m. Calculate the hypotenuse. Show working and give your answer to two decimal places.

3. Calculate the acute angle opposite the 3.00 m side in the triangle. Use trigonometry and give your answer to two decimal places (°).

4. Using the example design, calculate the total perimeter of the compound pool (outer edge). Show working and round to two decimal places. (Hint: the triangle shares the 3.00 m side with the rectangle.)

5. Calculate the total area of the compound pool in the example design. Show working and give the answer to two decimal places (m²).

6. Verify the minimum-angle safety rule: find the smallest interior angle in the compound shape (include triangle and quadrilateral angles). Is every angle ≥ 30°? Explain with your calculations.

7. Design your own pool outline that fits inside a 12 m by 8 m backyard. Your design must include one quadrilateral and one right-angled triangle. Draw your top-down plan and label all given and unknown sides and angles.

8. Choose one unknown side and one unknown angle from your design. Show full working to find each using Pythagoras and/or trigonometric ratios. State units and round to two decimal places.

9. State the total perimeter and total area of your pool design. Give answers with units and rounded to two decimal places.

10. Brief reflection: describe one design decision (e.g. changing an angle or side) and explain, in one or two sentences, how that change would affect area or perimeter.