1. **State the problem:** Calculate the area of the cross section of the slide, which is a right triangle with a stepped platform inside. 2. **Identify the dimensions:** - Height of the big triangle (vertical side): $3$ m - Base of the big triangle: sum of $0.5$ m (50 cm) + $1$ m + $1$ m = $2.5$ m 3. **Calculate the area of the big triangle:** The area formula for a triangle is $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ So, $$\text{Area}_{\text{big triangle}} = \frac{1}{2} \times 2.5 \times 3 = \frac{1}{2} \times 7.5 = 3.75\, m^2$$ 4. **Calculate the area of the stepped platform inside:** - First step: vertical height $1$ m, width $0.5$ m - Horizontal bar above first step: width $1.5$ m, height $1$ m (same height as first step) - Second vertical step down: height $0.5$ m, width $1.5$ m (horizontal bar width) - Horizontal bar to the right: width $2$ m, height $0.5$ m (height after second step) Calculate areas of each rectangular part: - First step rectangle: $1 \times 0.5 = 0.5\, m^2$ - Horizontal bar above first step: $1 \times 1.5 = 1.5\, m^2$ - Second vertical step down rectangle: $0.5 \times 1.5 = 0.75\, m^2$ - Horizontal bar to the right: $0.5 \times 2 = 1.0\, m^2$ 5. **Sum the areas of the stepped platform:** $$0.5 + 1.5 + 0.75 + 1.0 = 3.75\, m^2$$ 6. **Calculate the cross section area of the slide:** Since the stepped platform is inside the triangle, the cross section area is the area of the big triangle minus the area of the platform voids if any. But here, the platform is part of the slide, so the cross section area is the area of the big triangle. **Final answer:** $$\boxed{3.75\, m^2}$$