Question

1. find the area of $\triangle abc$.

(an equilateral triangle $abc$ with side $bc$ labeled 7 and marks indicating all sides are equal)

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle ABC \) has all sides marked as equal (the tick marks indicate equal sides), so it is an equilateral triangle with side length \( s = 7 \).

Step2: Recall the area formula for an equilateral triangle

The area \( A \) of an equilateral triangle with side length \( s \) is given by the formula:
\[
A=\frac{\sqrt{3}}{4}s^{2}
\]

Step3: Substitute the side length into the formula

Substitute \( s = 7 \) into the formula:
\[
A=\frac{\sqrt{3}}{4}\times(7)^{2}=\frac{\sqrt{3}}{4}\times49=\frac{49\sqrt{3}}{4}
\]

Answer:

The area of \( \triangle ABC \) is \( \frac{49\sqrt{3}}{4} \) (or approximately \( 21.22 \) if a decimal approximation is preferred).