Question

what is the area, in square feet, of the shape below? express your answer as a fraction in simplest form.
1/5 ft
4/5 ft

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = \frac{4}{5}\) ft and the height \(h=\frac{1}{5}\) ft.

Step2: Substitute the values into the formula

Substitute \(b = \frac{4}{5}\) and \(h=\frac{1}{5}\) into \(A=\frac{1}{2}\times b\times h\). So \(A=\frac{1}{2}\times\frac{4}{5}\times\frac{1}{5}\).

Step3: Multiply the fractions

First, multiply \(\frac{4}{5}\times\frac{1}{5}=\frac{4\times1}{5\times5}=\frac{4}{25}\). Then multiply by \(\frac{1}{2}\), so \(A=\frac{1}{2}\times\frac{4}{25}=\frac{1\times4}{2\times25}=\frac{4}{50}\).

Step4: Simplify the fraction

Simplify \(\frac{4}{50}\) by dividing both the numerator and denominator by their greatest - common divisor (GCD). The GCD of 4 and 50 is 2. So \(\frac{4\div2}{50\div2}=\frac{2}{25}\).

Answer:

\(\frac{2}{25}\) square feet