Exercise 7 Page 783

We are given that Marquez and Victoria are making pinwheels. Each of them is composed of $4$ triangles with the dimensions as shown below.

Using the given dimensions, we will find the perimeter and the area of this triangle. Let's start with the perimeter.

Perimeter

First let's recall that the perimeter is the sum of all side lengths of the figure. Therefore, to find the perimeter of a triangle we will add the lengths of all three sides. The perimeter of this triangle is $28.5$ inches.

Area

Now let's recall the formula for the area of a triangle. In this formula $b$ is the base and $h$ is the corresponding height. Let's look at the picture. We will label the height corresponding to the base that has a length of $9$ inches as $h.$ As we can see, $h$ is a leg of a right triangle, so we can find this value using the Pythagorean Theorem. Let's recall that according to this theorem the sum of the squared legs of a right triangle is equal to its squared hypotenuse. Now we will solve the above equation. Notice that since $h$ represents the height, we will consider only the positive case when taking the square root of $h^2.$ The height of the triangle is $7.5$ inches. Now we will substitute this value into the area formula and simplify. The area of this triangle is $33.75$ square inches.