1. The problem asks to find the area of each figure described. 2. For the right triangle inside a rectangle with hypotenuse 18 and one angle 30°: - Use the formula for the area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ - In a 30°-60°-90° triangle, the sides are in ratio 1 : \sqrt{3} : 2. - Hypotenuse = 18, so the shorter leg (opposite 30°) = $$\frac{18}{2} = 9$$. - The longer leg (height) = $$9 \sqrt{3}$$. - Area = $$\frac{1}{2} \times 9 \times 9 \sqrt{3} = \frac{81 \sqrt{3}}{2}$$. 3. For the L-shaped figure made of rectangles with dimensions 16 ft, 8 ft, and 4 ft, total area given as 160 ft²: - The area is the sum of the areas of the rectangles. - Confirming: $$16 \times 8 = 128$$ and $$4 \times 8 = 32$$. - Total area = $$128 + 32 = 160$$ ft². 4. For the complex polygon divided into rectangles with sides 12 cm, 8 cm, 4 cm, 3/4 cm, 6 cm, 2 cm and sub-calculations: - Calculate each rectangle's area: - $$4 \times 4 = 16$$ - $$4 \times 10 = 40$$ - $$8 \times 4 = 32$$ - Sum areas: $$16 + 40 + 32 = 88$$ cm². Final answers: - Area of right triangle = $$\frac{81 \sqrt{3}}{2}$$ - Area of L-shaped figure = 160 ft² - Area of complex polygon = 88 cm²