1. Problem: Calculate the area of a triangle with base $b=10$ units and height $h=6$ units. 2. Formula: The area $A$ of a triangle is given by $$A=\frac{1}{2} \times b \times h$$ 3. Substitute the values: $$A=\frac{1}{2} \times 10 \times 6$$ 4. Simplify: $$A=\frac{1}{2} \times 60$$ 5. Calculate: $$A=30$$ 6. Answer: The area of the triangle is 30 square units. --- 1. Problem: Find the circumference of a circle with radius $r=7$ units. 2. Formula: The circumference $C$ of a circle is $$C=2 \pi r$$ 3. Substitute the value: $$C=2 \pi \times 7$$ 4. Simplify: $$C=14 \pi$$ 5. Approximate: $$C \approx 14 \times 3.1416 = 43.9824$$ 6. Answer: The circumference is approximately 43.98 units. --- 1. Problem: Solve for $x$ in the equation $2x + 5 = 17$. 2. Subtract 5 from both sides: $$2x + 5 - 5 = 17 - 5$$ 3. Simplify: $$2x = 12$$ 4. Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{12}{2}$$ 5. Calculate: $$x = 6$$ 6. Answer: $x=6$. --- 1. Problem: Find the length of the hypotenuse $c$ of a right triangle with legs $a=3$ units and $b=4$ units. 2. Formula: Pythagorean theorem $$c=\sqrt{a^2 + b^2}$$ 3. Substitute values: $$c=\sqrt{3^2 + 4^2}$$ 4. Calculate squares: $$c=\sqrt{9 + 16}$$ 5. Sum inside root: $$c=\sqrt{25}$$ 6. Calculate square root: $$c=5$$ 7. Answer: The hypotenuse length is 5 units.