Answer:
3√7 ≈ 7.937 units²
Explanation:
You want to know the area of the isosceles triangle with congruent sides 4 units and base 6 units.
Heron's formula
The perimeter of the triangle is ...
P = 4 + 4 + 6 = 14
so the semiperimeter is ...
s = P/2 = 14/2 = 7
By Heron's formula, the area of the triangle is ...
A = √(s(s -a)(s -b)(s -c))
A = √(7(7 -4)(7 -4)(7 -6)) = 3√7
The area of the triangle is 3√7 ≈ 7.937 square units.
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Additional comment
You can also compute the area after finding the altitude (the length of the dashed line) using the Pythagorean theorem. The figure consists of two right triangles, each with leg 3 and hypotenuse 4. The missing leg (the triangle height) is then ...
h = √(4² -3²) = √7
The area is ...
A = 1/2bh = 1/2(6)(√7) = 3√7 . . . . square units