9514 1404 393
Answer:
120 m²
Step-by-step explanation:
If you divide the isosceles triangle into two right triangles, each has a leg and hypotenuse of 8 and 17, respectively. You may recognize these numbers as part of the Pythagorean triple (8, 15, 17). That recognition tells you the triangle's height is 15 m, so its area is ...
A = 1/2bh
A = 1/2(16 m)(15 m) = 120 m² . . . . triangle area
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Alternate solutions
Given the three sides, you can find the smallest angle from the Law of Cosines. It will be ...
α = arccos((17² +17² -16²)/(2·17·17)) ≈ 56.144°
Then the area is ...
A = 1/2·ab·sin(C) . . . for triangle with sides a, b, c and opposite angles A, B, C
A = 1/2sin(α)·17·17 = 120 . . . m²
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Using Heron's formula:
s = (17 +17 +16)/2 = 25
A = √(25(25 -17)(25 -17)(25 -16)) = 5×8×3 = 120 . . . m²
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If you need to, you can compute the triangle's height from the Pythagorean theorem.
a² +b² = c² . . . . generic Pythagorean theorem equation
8² + h² = 17² . . . with relevant values filled in
h² = 289 -64 = 225
h = √225 = 15
