Final answer:
To find the area of a triangle with given sides of 9cm, 7cm, and 12cm, we need to use the formula A = 1/2 * base * height. By identifying the largest side (12cm) as the base and using the Pythagorean theorem to find the height (10cm), we can calculate the area as 60cm^2.
Step-by-step explanation:
To find the area of a triangle, we can use the formula A = 1/2 * base * height. In this case, the given sides of the triangle are 9cm, 7cm, and 12cm. To determine the base and height of the triangle, we need to identify the largest side as the base, which is 12cm. Then, we can use the formula A = 1/2 * 12cm * h, where h is the height of the triangle. To find the height, we can use the Pythagorean theorem. We know that 9cm and 7cm are the other two sides of the triangle, so we can use a^2 + b^2 = c^2, where a = 7cm, b = 9cm, and c = 12cm. Substituting the values, we get 7^2 + 9^2 = 12^2. Simplifying, we find that 49 + 81 = 144, which is true. Therefore, the triangle is a right triangle, and the height can be found using the Pythagorean theorem, which is 10cm. Now that we have the base and height, we can calculate the area using A = 1/2 * 12cm * 10cm = 60cm^2. Therefore, the correct answer is D. 54.0 square cm.