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

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #65 : Triangles

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

Possible Answers:

18

12

10

20

9

Correct answer:

9

Explanation:

Sat-triangle

Sketching ABC in the xy-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 #141 : Triangles

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

Vt_p5

 

Possible Answers:

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

3h^{2}

4h^{2}

2h^{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 be 2h^{2}.

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