Find the area of a triangle with base 9 cm and height 7 cm?
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The area of a triangle is calculated using the formula: Area equals one-half times base times height. This formula works because a triangle is essentially half of a parallelogram or rectangle with the same base and height.
The base of a triangle can be any of its three sides. Once you choose a base, the height is the perpendicular distance from the opposite vertex to the line containing the base. This means the height might fall outside the triangle for obtuse triangles, but it's still perpendicular to the base.
Now let's apply the formula to a specific problem. We need to find the area of a triangle with a base of 9 centimeters and a height of 7 centimeters. First, we'll visualize the triangle with these dimensions clearly labeled.
Let's calculate the area step by step. First, we write down the formula. Then we substitute the given values: base equals 9 and height equals 7. Next, we multiply 9 by 7 to get 63. Finally, we multiply one-half by 63 to get 31.5. So the area is 31.5 square centimeters.
To verify our answer, let's visualize how the triangle relates to a rectangle. If we create a rectangle with the same base of 9 centimeters and height of 7 centimeters, its area would be 9 times 7, which is 63 square centimeters. Our triangle is exactly half of this rectangle, so its area is 63 divided by 2, which equals 31.5 square centimeters. This confirms our calculation.
There are alternative ways to verify our answer. One method is to count unit squares on a grid, though this gives an approximation. Another approach is to choose a different side as the base and measure the corresponding height. Regardless of which base-height pair we use, the area calculation will always yield the same result: 31.5 square centimeters. This consistency confirms the correctness of our solution.