1. Problem: Find the area of a rectangle with length $l=8$ and width $w=5$. 2. Formula: The area $A$ of a rectangle is given by $$A = l \times w$$ 3. Calculation: $$A = 8 \times 5 = 40$$ 4. Explanation: Multiply the length by the width to get the area. 1. Problem: Find the area of a triangle with base $b=10$ and height $h=6$. 2. Formula: The area $A$ of a triangle is $$A = \frac{1}{2} \times b \times h$$ 3. Calculation: $$A = \frac{1}{2} \times 10 \times 6 = 5 \times 6 = 30$$ 4. Explanation: Multiply base and height, then divide by 2. 1. Problem: Find the area of a circle with radius $r=7$. 2. Formula: The area $A$ of a circle is $$A = \pi r^2$$ 3. Calculation: $$A = \pi \times 7^2 = \pi \times 49 = 49\pi$$ 4. Explanation: Square the radius and multiply by $\pi$. 1. Problem: Find the area of a parallelogram with base $b=9$ and height $h=4$. 2. Formula: The area $A$ of a parallelogram is $$A = b \times h$$ 3. Calculation: $$A = 9 \times 4 = 36$$ 4. Explanation: Multiply base by height. 1. Problem: Find the area of a trapezoid with bases $b_1=8$, $b_2=5$ and height $h=6$. 2. Formula: The area $A$ of a trapezoid is $$A = \frac{1}{2} (b_1 + b_2) \times h$$ 3. Calculation: $$A = \frac{1}{2} (8 + 5) \times 6 = \frac{1}{2} \times 13 \times 6 = \cancel{\frac{1}{2}} \times 13 \times \cancel{6} = 13 \times 3 = 39$$ 4. Explanation: Add the two bases, multiply by height, then divide by 2.