To find the area of a triangle, you use the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
First, you need to convert the mixed numbers to improper fractions or decimals to work with them more easily.
Given:
- Base of the triangle: [tex]\( 10 \frac{3}{4} \text{ cm} \)[/tex]
- Height of the triangle: [tex]\( 15 \frac{3}{4} \text{ cm} \)[/tex]
Convert the base and the height to improper fractions:
[tex]\[ 10 \frac{3}{4} = 10 + \frac{3}{4} = 10.75 \text{ cm} \][/tex]
[tex]\[ 15 \frac{3}{4} = 15 + \frac{3}{4} = 15.75 \text{ cm} \][/tex]
Now, substitute these values into the area formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
[tex]\[ \text{Area} = \frac{1}{2} \times 10.75 \times 15.75 \][/tex]
To carry out the multiplication:
[tex]\[ 10.75 \times 15.75 = 169.3125 \][/tex]
Then, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 169.3125 = 84.65625 \text{ cm}^2 \][/tex]
So, the area of the triangle is [tex]\( 84.65625 \text{ cm}^2 \)[/tex].
