Asked by Story
On a coordinate plane, triangle R S T has points (negative 5, 6), (3, 4), and (negative 2, 2).
Which expression can be used to find the area of triangle RST?
(8 ∙ 4) - One-half (10 + 12 + 16)
(8 ∙ 4) - (10 + 12 + 16)
(8 ∙ 4) - One-half (5 + 6 + 8)
(8 ∙ 4) - (5 - 6 - 8)
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Answer: (8 ∙ 4) - One-half (10 + 12 + 16)
Reason: The triangle fits inside the rectangle with width 3 - (−5) = 8 and height 6 - 2 = 4, so rectangle area = 8·4. Subtract the three corner right-triangles with areas 1/2·(5·2), 1/2·(3·4), and 1/2·(8·2) = 5, 6, and 8 respectively (their doubled products are 10, 12, 16). So area = 8·4 − 1/2(10+12+16) = 32 − 19 = 13.
Reason: The triangle fits inside the rectangle with width 3 - (−5) = 8 and height 6 - 2 = 4, so rectangle area = 8·4. Subtract the three corner right-triangles with areas 1/2·(5·2), 1/2·(3·4), and 1/2·(8·2) = 5, 6, and 8 respectively (their doubled products are 10, 12, 16). So area = 8·4 − 1/2(10+12+16) = 32 − 19 = 13.
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