Question

1. find the perimeter and area of this triangle. dimensions are in centimeters.

Explanation:

Step1: Calculate the perimeter

The perimeter of a triangle is the sum of its three sides. The sides are 80 cm, 82 cm, and 18 cm.
$Perimeter = 80 + 82 + 18$
$Perimeter = 180$ cm

Step2: Check if it's a right triangle (to find area)

We can use the Pythagorean theorem: $a^2 + b^2 = c^2$. Let's check if $18^2 + 80^2 = 82^2$.
$18^2 = 324$, $80^2 = 6400$, $82^2 = 6724$.
$324 + 6400 = 6724$, which equals $82^2$. So it's a right triangle with legs 18 cm and 80 cm.

Step3: Calculate the area

The area of a right triangle is $\frac{1}{2} \times base \times height$. Here, base = 80 cm, height = 18 cm.
$Area = \frac{1}{2} \times 80 \times 18$
$Area = 40 \times 18$
$Area = 720$ $cm^2$

Answer:

Perimeter: 180 centimeters, Area: 720 square centimeters