Question

Describe the formula for the area of an obtuse triangle in word form.

a) Area = (1/2) × base × height
b) Area = (1/2) × product of two sides × sine of the included angle
c) Area = (1/2) × sum of two sides × distance between them
d) Area = product of three sides × cosine of one of the angles

Answer 1

For any triangle, including an obtuse one, the area formula is Area = (1/2) × base × height. The area of a triangle with base 1.007 m and height 0.665 m is 0.3343 m², reflecting four significant figures in accordance with the measurements provided.

Step-by-step explanation:

The formula for the area of an obtuse triangle or any triangle is given as Area = (1/2) × base × height. This formula can be applied regardless of the triangle's type, whether it is obtuse, acute, or right. Using this formula to calculate the area of a triangle with a base of 1.007 m and a height of 0.665 m, we first ensure that both measurements are in the same units, in this case, meters. Then, we apply the formula:

Area = (1/2) × 1.007 m × 0.665 m = 0.3343 m²

We also ensure that we express our final answer to the proper number of significant figures. Since our provided measurements have four significant figures maximum (found in the measurement 0.665 m), our final area should also reflect four significant figures: 0.3343 m².