refer to the figure to the right. find the area in acres of the property (enclosed by the right triangle) under the given assumptions.

the stream frontage is 800 feet in length and the property line is 3100 feet in length.

the lot has an area of about acre(s).
(round the final answer to the nearest hundredth as needed. round all intermediate values to the nearest whole number as needed.)

Question

refer to the figure to the right. find the area in acres of the property (enclosed by the right triangle) under the given assumptions.

the stream frontage is 800 feet in length and the property line is 3100 feet in length.

the lot has an area of about   acre(s).
(round the final answer to the nearest hundredth as needed. round all intermediate values to the nearest whole number 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": true, "concepts_used": [ "Pythagorean Theorem", "Triangle Area Calculation", "Acre Conversion" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Triangle Area Calculation", "Acre Conversion" ] } ## Find the missing leg of the right triangle Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} a^2 + b^2 &= c^2 \ 800^2 + b^2 &= 3100^2 \ 640000 + b^2 &= 9610000 \ b^2 &= 8970000 \ b &= \sqrt{8970000} \approx 2994.9958 \ b &\approx 2995 \text{ feet} \end{aligned} $$ ## Calculate the area of the triangular property Using the *Triangle Area Calculation* knowledge point $$ \begin{aligned} \text{Area} &= \frac{1}{2} \times \text{base} \times \text{height} \ \text{Area} &= \frac{1}{2} \times 800 \times 2995 \ \text{Area} &= 400 \times 2995 \ \text{Area} &= 1198000 \text{ square feet} \end{aligned} $$ ## Convert the area from square feet to acres Using the *Acre Conversion* knowledge point $$ \begin{aligned} 1 \text{ acre} &= 43560 \text{ square feet} \ \text{Area in acres} &= \frac{1198000}{43560} \ \text{Area in acres} &\approx 27.5023 \text{ acres} \ \text{Area in acres} &\approx 27.50 \text{ acres} \end{aligned} $$ The lot has an area of about 27.50 acre(s). { "elements": [ { "type": "polygon", "params": [ [0, 0], [8, 0], [0, -6] ], "properties": { "fillColor": "rgba(140, 85, 242, 0.3)", "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "A", "color": "#8C55F2", "withLabel": false } }, { "type": "point", "params": [[8, 0]], "properties": { "name": "B", "color": "#8C55F2", "withLabel": false } }, { "type": "point", "params": [[0, -6]], "properties": { "name": "C", "color": "#8C55F2", "withLabel": false } }, { "type": "text", "params": [4, 0.5, "Stream Frontage: 800 ft"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [4.5, -3.2, "Property Line: 3100 ft"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-2.5, -3, "b ≈ 2995 ft"], "properties": { "color": "#583C87" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the missing leg of the right triangle

Calculate the area of the triangular property

Convert the area from square feet to acres

Answer: