A triangle has a base of 8 cm and a height of 3 cm. The triangle is dilated by a scale factor of 3. Calculate and compare the areas of the dilated triangle and the original triangle.
To find the area of a triangle, you can use the formula:
Area = (base * height) / 2.
The original triangle has a base of 8 cm and a height of 3 cm. Let's calculate its area first:
Area of the original triangle = (8 cm * 3 cm) / 2 = 24 cm^2.
Next, to determine the area of the dilated triangle, we need to find the new base and height values. Since the triangle is dilated by a scale factor of 3, both the base and height will be multiplied by 3.
New base = 8 cm * 3 = 24 cm.
New height = 3 cm * 3 = 9 cm.
Now we can calculate the area of the dilated triangle using the same formula:
Area of the dilated triangle = (24 cm * 9 cm) / 2 = 108 cm^2.
Comparing the areas of the original and dilated triangles, we have:
Area of original triangle = 24 cm^2.
Area of dilated triangle = 108 cm^2.