a triangular lot is 120 ft on one side and has a property line of length 900 ft. find the area of the lot in acres. (figure not drawn to scale)

area = acre(s)
(round to the nearest hundredth as needed.)

Question

a triangular lot is 120 ft on one side and has a property line of length 900 ft. find the area of the lot in acres. (figure not drawn to scale)

area =   acre(s)
(round to the nearest hundredth as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Triangle Area Calculation", "Acre Conversion" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Triangle Area Calculation", "Acre Conversion" ] } ## Find the missing side of the right triangle Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} a^2 + b^2 &= c^2 \ 120^2 + b^2 &= 900^2 \ 14400 + b^2 &= 810000 \ b^2 &= 795600 \ b &= \sqrt{795600} \approx 891.9641 \text{ ft} \end{aligned} $$ ## Calculate the area of the triangular lot Using the *Triangle Area Calculation* knowledge point $$ \begin{aligned} \text{Area} &= \frac{1}{2} \times \text{base} \times \text{height} \ \text{Area} &= \frac{1}{2} \times 120 \times \sqrt{795600} \ \text{Area} &= 60 \times \sqrt{795600} \approx 53517.8474 \text{ sq ft} \end{aligned} $$ ## Convert the area to acres Using the *Acre Conversion* knowledge point $$ \begin{aligned} 1 \text{ acre} &= 43560 \text{ sq ft} \ \text{Area in acres} &= \frac{53517.8474}{43560} \approx 1.2286 \text{ acres} \ \text{Area} &\approx 1.23 \text{ acres} \end{aligned} $$ Area = $1.23$ acre(s) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Find the missing side of the right triangle

Calculate the area of the triangular lot

Convert the area to acres

Answer: