What is the solution with steps---**Overall Context:**
MATH WORKBOOK
Section: Triangles and Quadrilaterals
**Question 6:**
**Question Stem:**
If AB=AC=BC=14 cm, what is the area of triangle ABC in cm²?
**Options:**
A) 144
B) $25\sqrt{3}$
C) $25\sqrt{3}$
D) $49\sqrt{3}$
**Chart/Diagram Description:**
Type: Geometric figure (Triangle)
Main Elements:
* Vertices: Labeled A (top), C (bottom left), B (bottom right).
* Lines: Three straight lines forming the sides of the triangle (AB, BC, AC).
* Labels: The side BC is labeled with the number "14". The vertices are labeled A, B, and C.
(Note: The diagram shows a general triangle labeled with vertices A, B, C and side length 14 on BC. The question stem specifies that AB=AC=BC=14 cm, indicating it is an equilateral triangle with side length 14 cm).
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We have a triangle ABC where all three sides are equal to 14 centimeters. Since all sides are equal, this is an equilateral triangle. We need to find its area.
For an equilateral triangle, we use the formula: Area equals square root of 3, divided by 4, times the side length squared. Since all sides are equal, we label each side as 'a'.
Now we substitute the given side length of 14 centimeters into our formula. First, we replace 'a' with 14. Then we calculate 14 squared, which equals 196. Finally, we substitute this value back into our formula.
Now we simplify the expression. We have 196 square root of 3, divided by 4. Since 196 divided by 4 equals 49, our final answer is 49 square root of 3 square centimeters. This corresponds to option D.
Let's verify our answer by checking the multiple choice options. We calculated 49 square root of 3 square centimeters, which matches option D exactly. Therefore, the correct answer is D.