To find the area of a triangle using the given sides of the triangle, we can use the formula:
Area = 0.5 * base * height
First, we need to find the height of the triangle. We can use the Pythagorean theorem to find the height. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
hypotenuse^2 = base^2 + height^2
144^2 = 7^2 + 4^2
20736 = 49 + 16
20736 = 65
Now, we can solve for the height:
height^2 = 20736 - 49 - 16
height^2 = 20736 - 65
height^2 = 20671
height = sqrt(20671)
height ≈ 143.8
Now that we have the height, we can calculate the area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 7 * 143.8
Area = 0.5 * 1006.6
Area ≈ 503.3 square inches
Therefore, the area of the triangle is approximately 503.3 square inches.
Find the area of each figure round your answer to the nearest tenth
Hypotenuse side of the triangle is 144 degrees
Bigger side of the triangle is 7 inches
Smaller side of the triangle is 4 inches
Show all your work to support your answer
1 answer