Subjects geometry

Triangular Lot Cost 6A1899

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1. **State the problem:** We need to find the area of a triangular lot with sides 188 ft, 87 ft, and 167 ft, then calculate the cost at 3 per square foot. 2. **Formula used:** Use Heron's formula for the area of a triangle given sides $a$, $b$, and $c$: $$s = \frac{a+b+c}{2}$$ $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$ where $s$ is the semi-perimeter. 3. **Calculate the semi-perimeter:** $$s = \frac{188 + 87 + 167}{2} = \frac{442}{2} = 221$$ 4. **Calculate the area:** $$\text{Area} = \sqrt{221(221-188)(221-87)(221-167)} = \sqrt{221 \times 33 \times 134 \times 54}$$ 5. **Calculate the product inside the square root:** $$221 \times 33 = 7293$$ $$7293 \times 134 = 977862$$ $$977862 \times 54 = 52704548$$ 6. **Calculate the square root:** $$\text{Area} = \sqrt{52704548} \approx 7261.15 \text{ square feet}$$ 7. **Calculate the cost:** $$\text{Cost} = 7261.15 \times 3 = 21783.45$$ **Final answer:** The lot costs 21783.45.