In a triangle ABC, AC=24 cm, BC=30 cm, and m∠C=40°. Determine the area of the triangle. Round to nearest square centimeter.

The area of the triangle is 231 cm² to the nearest square centimeter

Step-by-step explanation:

We can find the area of a triangle has the lengths of two sides and the measure of the included angle by using the trigonometry

A = × s1 × s2 × sinФ, where

In ΔABC

∵ AC = 24 cm

∴ s1 = 24

∵ BC = 30 cm

∴ s2 = 30

∵ m∠C = 40°

∴ Ф = 40°

→ By using the rule of the area above

∵ A = × 24 × 30 × sin(40°)

∴ A = 231.4035395 cm²

→ Round it to the nearest square centimeter

∴ A = 231 cm²

∴ The area of the triangle is 231 cm² to the nearest square centimeter

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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