The lengths of the triangle are rounded to the nearest 0.1 cm

The lengths of the triangle shown below are rounded to the nearest 0.1 cm. What is the area, to the nearest 1 cm2, of this triangle?

(Note: The area of any triangle with sides of length a, b, and c opposite angles of measure A, B, and C, respectively, is given by 1/2 ab sin C.)

  1. 4
  2. 5
  3. 8
  4. 10
  5. 14


The correct answer is C.

Area of the triangle = 1/2 ab sin C

Since only one angle measure is given in the triangle, use that for C in the formula.

Area = 1/2 ab sin 30°

The length of the side opposite from angle C, the 30° angle, is 5.0 cm and must correspond to side c. That means that the other side lengths, 8.0 cm and 4.0 cm, correspond to sides a and b.

So, area =  1/2 x (8.0) x (4.0) x sin 30°

Since, sine 30° = 1/2

Area = 8 cm2