Find area of triangle. 18cm and 12cm.?

To find the area of a triangle with base 18cm and height 12cm, you can use the formula:

Area = 1/2 * base * height

Plugging in the values:

Area = 1/2 * 18cm * 12cm
Area = 1/2 * 216cm
Area = 108cm

Therefore, the area of the triangle is 108 square centimeters.

Step 1: Calculate the height (h) of the triangle.

To do this, we can use the formula:

```
h = √(s-(s-a)-(s-b)-(s-c))
```

where:

- s = (a + b + c) / 2 is the semiperimeter of the triangle
- a, b, c are the lengths of the sides of the triangle

In this case, a = 18cm and b = 12cm. We don't know the length of c yet, so let's call it c.

```
s = (18cm + 12cm + c) / 2
```

We don't have the value of c, so we can't calculate s and h yet.

Step 2: Use the Pythagorean Theorem to find c.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we can use the Pythagorean Theorem on the right triangle formed by sides a, b, and c.

```
a² + b² = c²
```

Plugging in the values we know:

```
(18cm)² + (12cm)² = c²
324cm² + 144cm² = c²
468cm² = c²
c = √468cm²
c = 21.6cm
```

Step 3: Calculate the area of the triangle.

Now that we know the length of all three sides, we can use the formula for the area of a triangle:

```
A = (1/2) - b - h
```

Plugging in the values we know:

```
A = (1/2) - 12cm - h
```

We don't have the value of h yet, so we can't calculate the area yet.

Going back to Step 1:

Now that we know the length of side c, we can calculate the semiperimeter:

```
s = (18cm + 12cm + 21.6cm) / 2
s = 25.8cm
```

Now we can calculate the height:

```
h = √(25.8cm-(25.8cm-18cm)-(25.8cm-12cm)-(25.8cm-21.6cm))
h ≈ 16.8cm
```

Finally, we can calculate the area:

```
A = (1/2) - 12cm - 16.8cm
A ≈ 100.8cm²
```

Therefore, the area of the triangle is approximately 100.8cm².