Finding perimeter and area of the triangle with a missing base

Perimeter = 26.584 un.

Area = 31.752 un².

Step-by-step explanation:

Given the image of the figure, when the height is added to the triangle, the resulting figures are two right triangles since a 90° angle is formed.  Since there is a right triangle where two sides are known, you can use the Pythagorean Thereom to solve for the missing side.  The formula for the Pythagorean Thereom:  a² + b² = c², where 'a' and 'b' represents the sides (height and base) of the triangle and 'c' represents the hypotenuse (diagonal).  To solve for the missing side, we put are known values into the equation:

6² + b² = 8²  or 36 + b² = 64 or 36 - 36 + b² = 64 - 36 or b² = 28

Take the square root of both sides:  √b² = √28 or b≈5.292

Since this measurement would be for only one of the two right triangles formed from the height, the base of the entire larger triangle is (5.292)(2) = 10.584.  

The formula for Perimeter of a triangle is the sum of all sides:  8 + 8 + 10.584 = 26.584 u.

The formula for Area of a triangle is: A = 1/2bh, where A = area, b = base and h  = height:  A = (1/2)(10.584)(6) = 31.752 u².

maybe - definition of supplementary angles. im not sure. sorry

step-by-step explanation: