Question

Round to the nearest decimal place if needed.Find the area & perimeter.

Answer 1

SOLUTION.

The shape below is a triangle. We are told to find the area and perimeter.

Let's find the area first

`\begin{gathered} \text{Area of a triangle is given as } \\ A=(1)/(2)* b* h \\ \text{where b = base = 15 yd} \\ h\text{ = height = 12 yd} \\ A=(1)/(2)* b* h \\ \\ A=(1)/(2)*15*12 \\ \\ A=15*6 \\ A=90yd^2 \end{gathered}`

For the perimeter, we have to find the other side of the triangle. This side is the longest side, known as the hypotenuse.

To find this side, we will make use of the Pythagoras theorem

The Pythagoras theorem states that the square of the longest side is equal to the sum of the squares of the other two sides

Now let the longest side be x, then from Pythagoras we have

`\begin{gathered} x^2=12^2+15^2 \\ x^2=144+225 \\ x^2=369 \\ x=\sqrt[]{369} \\ x=\text{ 19.2 yd} \end{gathered}`

Perimeter is the distance around a plane shape. So to find the perimeter, we add all the sides of the triangle

Perimiter = 12 + 15 + 19.2 = 46.2 yd

Therefore, the area of the shape is 90 square yards and the Perimeter is 46.2 yards