A triangle has base 100 ft and perpendicular height 80 ft. What is its area in square feet?
Correct Answer
C) 4,000 square feet
Triangle area=(100 ft×80 ft)/2=4000 square feet. Common errors: not halving base × height gives 8,000 square feet; adding the dimensions instead of multiplying them gives 180 square feet; dividing by 4 instead of 2 gives 2,000 square feet.
Why This Is the Correct Answer
Option C is correct because the area is (100 ft × 80 ft) ÷ 2 = 4,000 square feet. The height is perpendicular to the base, so the standard one-half base times height formula applies directly.
Why the Other Options Are Wrong
Option A: 180 square feet
Option A is wrong because 180 square feet comes from adding the dimensions (100 + 80) instead of multiplying them. The correct area is (100 × 80) ÷ 2 = 4,000 square feet.
Option B: 2,000 square feet
Option B is wrong because 2,000 square feet comes from dividing by 4 instead of 2 (100 × 80 ÷ 4). The correct area is (100 × 80) ÷ 2 = 4,000 square feet.
Option D: 8,000 square feet
Option D is wrong because 8,000 square feet is base times height (100 × 80) without halving it, which is the area of a rectangle with those sides. A triangle is half of that: 8,000 ÷ 2 = 4,000 square feet.
Triangle is half a rectangle
Picture a rectangle with the same base and height, then cut it diagonally; the triangle is half of it.
How to use: Use this to remember to divide by 2 when finding a triangle's area.
Exam Tip
Make sure the height given is perpendicular to the base before applying one-half base times height.
Common Mistakes to Avoid
- -Forgetting to divide base times height by 2
- -Adding the dimensions instead of multiplying
- -Using a slanted side instead of the perpendicular height
Concept Deep Dive
Analysis
This question tests the formula for the area of a triangle. The area equals one-half of the base times the perpendicular height. The base and height must be multiplied, then the product halved.
Background Knowledge
Appraisers often compute areas of lots and building sections made of rectangles and triangles. A triangle's area is one-half of the base multiplied by the height measured perpendicular to that base. Using the correct formula for each shape is key to accurate site and building measurements.
Real-World Application
An appraiser calculates the area of a pie-shaped lot by splitting it into a rectangle and a triangle. The triangular portion has a 100-foot base and 80-foot perpendicular depth, so the appraiser adds 4,000 square feet for that part.
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