Question

match each figure to the most appropriate formula for solving its area. choose... choose...

Explanation:

Step1: Identify the first triangle

The first triangle has all - sides equal (5 cm each), so it is an equilateral triangle. The formula for the area of an equilateral triangle is $A=\frac{\sqrt{3}}{4}a^{2}$, where $a$ is the side - length. Here, $a = 5$ cm.

Step2: Identify the second triangle

The second triangle has two sides and the included angle given. The formula for the area of a triangle when two sides $b$ and $c$ and the included angle $A$ are known is $A=\frac{1}{2}bc\sin A$. Here, $b = 6.5$ m, $c = 4.9$ m, and $A = 96^{\circ}$.

Answer:

For the equilateral triangle with side $a = 5$ cm, the area formula is $A=\frac{\sqrt{3}}{4}a^{2}$. For the triangle with sides $b = 6.5$ m, $c = 4.9$ m and included angle $A = 96^{\circ}$, the area formula is $A=\frac{1}{2}bc\sin A$.