PSAT Math : How to find the area of an acute / obtuse triangle

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #141 :Sat Mathematics

If triangle ABC has vertices (0, 0), (6, 0), and (2, 3) in thexy-plane, what is the area of ABC?

Possible Answers:

12

20

9

18

10

Correct answer:

9

Explanation:

Sat-triangle

Sketching ABC in thexy-plane, as pictured here, we see that it has base 6 and height 3. Since the formula for the area of a triangle is 1/2 * base * height, the area of ABC is 1/2 * 6 * 3 = 9.

Example Question #4 :How To Find The Area Of An Acute / Obtuse Triangle

The height,, of trianglein the figure is one-fourth the length of. In terms of h, what is the area of triangle?

Vt_p5

Possible Answers:

\frac{1}{2}h^{2}

2h^{2}

3h^{2}

h^{2}

Correct answer:

2h^{2}

Explanation:

If\dpi{100} \small h=\frac{1}{4}*\dpi{100} \small \overline{PQ}, then the length of\dpi{100} \small \overline{PQ}must be\dpi{100} \small 4h.

Using the formula for the area of a triangle (\frac{1}{2}bh), with\dpi{100} \small b=4h, the area of the triangle must be2h^{2}.

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