Mathematics 10 — Exercise Review · Q10, area

Full question

A sector of a circle has radius 5 cm and perimeter 16 cm. Find the area of the sector.

Step-by-step solution

1. Use area=½rl.

2. Substitute the given numbers into the formula.

   $$\frac{1}{2}\times 5\times 6$$

3. Calculate this operation before combining the remaining terms.

   $$1\times 5\times 6=30$$

4. Calculate this operation before combining the remaining terms.

   $$2\times 1\times 1=2$$

5. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{30\times 1}{1\times 2}$$

6. Calculate this operation before combining the remaining terms.

   $$30\times \frac{1}{2}=15$$

7. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{1\times 5\times 6}{2\times 1\times 1}$$

8. Calculate these two products separately.

   $$\frac{30}{2}$$

9. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

   $$\mathrm{GCD}=2$$

10. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{2\times 1}{1\times 2}$$

11. Calculate these two products separately.

    $$\frac{2}{2}$$

12. Show the two divisions explicitly.

    $$\frac{\frac{2}{2}}{\frac{2}{2}}$$

13. Write the reduced fraction.

    $$\frac{1}{1}$$

14. Calculate this operation before combining the remaining terms.

    $$2\times \frac{1}{2}=1$$

15. Calculate this operation before combining the remaining terms.

    $$\frac{1}{1}=1$$

16. Calculate this operation before combining the remaining terms.

    $$15\times 1=15$$

17. Show the two divisions explicitly.

    $$\frac{\frac{30}{2}}{\frac{2}{2}}$$

18. Evaluate the numerator division.

    $$\frac{30}{2}=15$$

19. Evaluate the denominator division.

    $$\frac{2}{2}=1$$

20. Write the reduced fraction.

    $$15\times \frac{1}{1}$$

21. Calculate this operation before combining the remaining terms.

    $$\frac{1}{2}\times 5\times 6=15$$

22. The required result is shown below. Unit: cm²

    $$15$$

Answer

The final answer is shown below.