find the perimeter and area of each figure. Give your answers in simplest radical form.
1. a 30 degree-60 degree-90 degree triangle with hypotenuse length 28 centimeters
hypot=28
opposide 30 angle= 14
adjacent to 30 angle= 14sqrt3
area= 1/2 bh = 1/2 * 14*14sqrt3
perimeter: add sides
To find the perimeter and area of a triangle, we need to know the lengths of its sides.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
Side opposite the 30-degree angle : Side opposite the 60-degree angle : Hypotenuse = 1 : √3 : 2
Given the hypotenuse length of 28 centimeters, we can use this ratio to find the lengths of the other sides.
Side opposite the 30-degree angle = (1/2) * hypotenuse = (1/2) * 28 = 14 centimeters
Side opposite the 60-degree angle = (√3/2) * hypotenuse = (√3/2) * 28 = 14√3 centimeters
Now we can find the perimeter:
Perimeter = Length of side opposite 30-degree angle + Length of side opposite 60-degree angle + Hypotenuse
= 14 centimeters + 14√3 centimeters + 28 centimeters
= 42 + 14√3 centimeters
To find the area of the triangle, we can use the formula:
Area = (1/2) * base * height
In a 30-60-90 triangle, the base is the side opposite the 60-degree angle, and the height is the side opposite the 30-degree angle. So, the area can be calculated as:
Area = (1/2) * (14√3 centimeters) * (14 centimeters)
= (1/2) * (14 * 14) * √3
= 98√3 square centimeters
Therefore, the perimeter of the triangle is 42 + 14√3 centimeters, and the area is 98√3 square centimeters.