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Lines, Angles, and Triangles

SAT Math· difficulty 5/5

Equilateral triangle ABC has side length 6. Point D is on BC such that AD is perpendicular to BC. What is the area of triangle ABD?

  • A

    934\frac{9\sqrt{3}}{4}

  • B

    333\sqrt{3}

  • C

    932\frac{9\sqrt{3}}{2}

    check_circle
  • D

    939\sqrt{3}

Explanation

AD is the altitude, so AD=3sqrt3AD = 3\\sqrt{3}. BD = 3 (half of BC). Area =frac12(3)(3sqrt3)=frac9sqrt32= \\frac{1}{2}(3)(3\\sqrt{3}) = \\frac{9\\sqrt{3}}{2}.

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