Question

finding perimeter, circumference, and area find the perimeter (or circumference) and area of the figure. (where necessary, use π ≈ 3.14.) 19. right triangle with one leg 5, another leg 5, hypotenuse 5√2

Explanation:

Step1: Identify the figure type

The figure is a right - triangle with legs of length \(a = 5\) and \(b = 5\), and hypotenuse \(c=5\sqrt{2}\).

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is the sum of the lengths of its three sides. So \(P=a + b + c\).
Substitute \(a = 5\), \(b = 5\), and \(c = 5\sqrt{2}\) into the formula:
\(P=5 + 5+5\sqrt{2}=10 + 5\sqrt{2}\approx10 + 5\times1.414=10 + 7.07 = 17.07\)

Step3: Calculate the area

The area \(A\) of a right - triangle is given by the formula \(A=\frac{1}{2}\times\text{base}\times\text{height}\). For a right - triangle, the two legs can be considered as the base and the height. Here, base \(= 5\) and height \(= 5\).
So \(A=\frac{1}{2}\times5\times5=\frac{25}{2}=12.5\)

Answer:

Perimeter: \(\boldsymbol{10 + 5\sqrt{2}\approx17.07}\) (or exact form \(10 + 5\sqrt{2}\)); Area: \(\boldsymbol{12.5}\)