1. **Problem Statement:** We have 6 pink tiles and 6 green tiles, each triangular with given side lengths. Pink tile sides: 7 m, 8 m, 13 m. Green tile sides: 13 m, 7 m, 10 m. We need to find the total area of pink and green tiles and then calculate the total cost based on given rates. 2. **Formula Used:** To find the area of a triangle with sides $a$, $b$, and $c$, we use Heron's formula: $$s = \frac{a+b+c}{2}$$ $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$ where $s$ is the semi-perimeter. 3. **Calculate area of one pink tile:** Sides: $a=7$, $b=8$, $c=13$ $$s = \frac{7+8+13}{2} = \frac{28}{2} = 14$$ $$\text{Area}_{pink} = \sqrt{14(14-7)(14-8)(14-13)} = \sqrt{14 \times 7 \times 6 \times 1} = \sqrt{588}$$ $$\sqrt{588} \approx 24.2487 \text{ m}^2$$ 4. **Calculate area of one green tile:** Sides: $a=13$, $b=7$, $c=10$ $$s = \frac{13+7+10}{2} = \frac{30}{2} = 15$$ $$\text{Area}_{green} = \sqrt{15(15-13)(15-7)(15-10)} = \sqrt{15 \times 2 \times 8 \times 5} = \sqrt{1200}$$ $$\sqrt{1200} \approx 34.6410 \text{ m}^2$$ 5. **Calculate total area for all tiles:** Pink tiles total area: $$6 \times 24.2487 = 145.4922 \text{ m}^2$$ Green tiles total area: $$6 \times 34.6410 = 207.8460 \text{ m}^2$$ 6. **Calculate total cost:** Cost per m² for pink tile = 4 Cost per m² for green tile = 6 Total cost for pink tiles: $$145.4922 \times 4 = 581.9688$$ Total cost for green tiles: $$207.8460 \times 6 = 1247.076$$ **Final answers:** - Total area of pink tiles = $145.49$ m² (rounded to 2 decimals) - Total area of green tiles = $207.85$ m² (rounded to 2 decimals) - Total cost of pink tiles = Rs. $581.97$ - Total cost of green tiles = Rs. $1247.08$