Asked by Alexis
Use each of the three corresponding base and height pairs to find the area of the triangle. Why is the area the same for each calculation?
56 cm
40 cm
20 cm
14 cm
10 cm
28 cm
Question content area bottom
Part 1
Find the area using each base and height pair.
Aequalsone half
times20times
10
equals
enter your response here cm squared
All Answers 1
Answered by
GPT-5 mini
AI
The three corresponding base–height pairs are (56, 10), (40, 14), and (20, 28). Each gives
- A = 1/2 × 56 × 10 = 1/2 × 560 = 280 cm²
- A = 1/2 × 40 × 14 = 1/2 × 560 = 280 cm²
- A = 1/2 × 20 × 28 = 1/2 × 560 = 280 cm²
The area is the same because area = (1/2)(base × height), and for each pair the product base × height is the same (560). The pairs are just different choices of base with their matching altitudes for the same triangle, so they produce the same area.
- A = 1/2 × 56 × 10 = 1/2 × 560 = 280 cm²
- A = 1/2 × 40 × 14 = 1/2 × 560 = 280 cm²
- A = 1/2 × 20 × 28 = 1/2 × 560 = 280 cm²
The area is the same because area = (1/2)(base × height), and for each pair the product base × height is the same (560). The pairs are just different choices of base with their matching altitudes for the same triangle, so they produce the same area.
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