What is the area, in square meters, of the shape below? Express your answer as a fraction in simplest form.
Understand the Problem
The question is asking us to calculate the area of a triangle given its height and the length of its base. The base is represented as 4/5 m and the height as 1/3 m. We will apply the formula for the area of a triangle, which is 1/2 * base * height.
Answer
The area of the triangle is $\frac{2}{15}$ square meters.
Answer for screen readers
The area of the triangle is $\frac{2}{15}$ square meters.
Steps to Solve
- Identify the formula for the area of a triangle
The area $A$ of a triangle can be calculated using the formula: $$ A = \frac{1}{2} \times \text{base} \times \text{height} $$
- Substitute the given values
Here, the base is $\frac{4}{5}$ m and the height is $\frac{1}{3}$ m. Substitute these values into the formula: $$ A = \frac{1}{2} \times \frac{4}{5} \times \frac{1}{3} $$
- Calculate the area
First, multiply the fractions: $$ A = \frac{1}{2} \times \frac{4}{5} \times \frac{1}{3} = \frac{1 \times 4 \times 1}{2 \times 5 \times 3} = \frac{4}{30} $$
- Simplify the fraction
To simplify $\frac{4}{30}$, divide both the numerator and the denominator by their greatest common divisor, which is 2: $$ A = \frac{4 \div 2}{30 \div 2} = \frac{2}{15} $$
The area of the triangle is $\frac{2}{15}$ square meters.
More Information
The area of a triangle can be found using its base and height, and expressing the answer in simplest form helps to clarify the value.
Tips
- Forgetting to multiply the base and height together before dividing by 2.
- Not simplifying the fraction to its simplest form once calculated.
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