To find the area of a triangle, you'll need to use the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Here’s a step-by-step solution:
1. Identify the base and height:
- The base of the triangle is given as 5 inches.
- The height is given as [tex]\(3 \frac{3}{4}\)[/tex] inches. This is a mixed number and needs to be converted to a decimal for easier calculation.
2. Convert the mixed number height to a decimal:
- A mixed number [tex]\(3 \frac{3}{4}\)[/tex] can be broken down into a whole number part and a fractional part.
- The whole number part is 3.
- The fractional part is [tex]\(\frac{3}{4}\)[/tex].
3. Convert the fractional part to a decimal:
- [tex]\(\frac{3}{4}\)[/tex] can be converted to a decimal by dividing 3 by 4.
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
4. Add the decimal to the whole number:
- [tex]\(3 + 0.75 = 3.75\)[/tex]
- So, the height in decimal form is 3.75 inches.
5. Apply the formula for the area of a triangle:
- Substitute the base (5 inches) and the height (3.75 inches) into the area formula:
[tex]\[ \text{Area} = \frac{1}{2} \times 5 \times 3.75 \][/tex]
6. Calculate the area:
- First, multiply the base and height:
[tex]\[ 5 \times 3.75 = 18.75 \][/tex]
- Then, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 18.75 = 9.375 \][/tex]
Therefore, the area of the triangle is [tex]\(9.375\)[/tex] square inches.
