How do u find the lateral area of a 3-sided 1-based triangle with a slant height of 7 and a height of 5?
To find the lateral area of a 3-sided 1-based triangle with a slant height and height given, you need to first find the base length. Here's a step-by-step explanation of how to calculate the lateral area:
1. Recall that the lateral area of a triangle is the sum of the areas of its three lateral faces.
2. Determine the base length of the triangle. In a 3-sided triangle, if the base is given as 1, then the length of each of the two equal sides can be found using the Pythagorean Theorem.
3. Apply the Pythagorean Theorem to find the length of the two equal slant sides.
a. The formula is c^2 = a^2 + b^2, where c is the hypotenuse (slant height) and a and b are the other two sides.
b. Plug in the values: c = 7 and a = b = 1 (since the base of the triangle is given as 1).
c. Use the equation to find the length of the slant sides: 7^2 = 1^2 + b^2.
d. Simplify the equation: 49 = 1 + b^2.
e. Solve for b: b^2 = 49 - 1 = 48.
f. Take the square root of both sides: b = √48 ≈ 6.93 (rounded to two decimal places).
4. Calculate the area of each lateral face of the triangle. Since the triangle is isosceles, these areas will be identical.
a. Use the formula for the area of a triangle: A = 0.5 * base * height.
b. The base length is 1, and the height is 5. So the area of each lateral face is: A = 0.5 * 1 * 5 = 2.5 square units.
5. Multiply the area of one lateral face by 3 to account for all three faces.
a. The lateral area of the triangle is: 3 * 2.5 = 7.5 square units.
Therefore, the lateral area of the 3-sided 1-based triangle with a slant height of 7 and a height of 5 is 7.5 square units.