Find the area of a triangle with base 7 cm and height 5 cm?
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The area of a triangle is given by 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 that base. This means the height line always forms a right angle with the base, regardless of the triangle's orientation.
Now let's apply the formula to a specific problem. We need to find the area of a triangle with a base of 7 centimeters and a height of 5 centimeters. First, we'll draw the triangle and clearly label these dimensions.
Let's substitute our values into the formula. Area equals one-half times base times height, which is one-half times 7 times 5. First, we multiply 7 by 5 to get 35. Then we multiply 35 by one-half, which gives us 17.5. Including the units, the area is 17.5 square centimeters.
To visually verify our answer, let's compare the triangle to a rectangle with the same base and height. The rectangle's area is base times height, which is 7 times 5 equals 35 square centimeters. As we can see, our triangle perfectly fits inside this rectangle and takes up exactly half of its area, confirming that 17.5 square centimeters is correct.
There are several equivalent ways to perform this calculation. We can write it as one-half times seven times five, or as seven times five divided by two, or as zero point five times seven times five. All these expressions are mathematically identical and will give us the same result of 17.5 square centimeters.
Let's practice with a few more examples. For a triangle with base 6 centimeters and height 4 centimeters, the area is 12 square centimeters. For base 10 centimeters and height 3 centimeters, the area is 15 square centimeters. And for base 8 centimeters and height 2.5 centimeters, the area is 10 square centimeters. In each case, we're applying the same fundamental formula.