Question

find the area of the triangle shown below.
6(\frac{1}{2}) in
5 in (with a right angle)
11(\frac{1}{10}) in
8(\frac{3}{5}) in
note: figure may not be drawn to scale.

Explanation:

Step1: Recall the formula for the area of a triangle

The area \( A \) of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base is \( 11\frac{1}{10} \) inches and the height is 5 inches.

Step2: Convert the mixed number to an improper fraction (optional, but helpful)

First, convert \( 11\frac{1}{10} \) to an improper fraction. \( 11\frac{1}{10}=\frac{11\times10 + 1}{10}=\frac{111}{10} \).

Step3: Substitute into the area formula

Using the formula \( A=\frac{1}{2}\times\text{base}\times\text{height} \), substitute base \( =\frac{111}{10} \) and height \( = 5 \). So, \( A=\frac{1}{2}\times\frac{111}{10}\times5 \).

Step4: Simplify the expression

Simplify \( \frac{1}{2}\times\frac{111}{10}\times5 \). The 5 and 10 can be simplified: \( \frac{5}{10}=\frac{1}{2} \). So the expression becomes \( \frac{1}{2}\times\frac{111}{2}=\frac{111}{4} \).

Step5: Convert back to a mixed number (if needed)

\( \frac{111}{4}=27\frac{3}{4} \) square inches. Alternatively, we can also do the calculation using decimals. \( 11\frac{1}{10}=11.1 \), then \( A = \frac{1}{2}\times11.1\times5 \). First, \( 11.1\times5 = 55.5 \), then \( \frac{1}{2}\times55.5 = 27.75 \), and \( 27.75 = 27\frac{3}{4} \).

Answer:

The area of the triangle is \( 27\frac{3}{4} \) square inches (or \( 27.75 \) square inches).