Core Connections: Course 2
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2. Section 1.2
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Exercise 129 Page 56

Practice makes perfect

We want to find the area and perimeter of the given figure. Let's start by identifying our figure!

Our figure is a quadrilateral with two pairs of parallel sides, which makes it a parallelogram. Now we can find the area and perimeter of the parallelogram one at a time.

Area

The area of a parallelogram is the product of its base and its height. In the given parallelogram, if we consider the side with a length of 57 inches as the base, then its corresponding height is 36 inches. Let's substitute these values into the formula for the area of a parallelogram and simplify.
A=bh
A= 57( 36)
A=2052
The area of the parallelogram is 2052 square inches.

Perimeter

The perimeter of a parallelogram is calculated by adding its four side lengths.

We can see that the parallelogram has side lengths of 57 and 41 inches. Now, recall that the opposite sides of parallelograms are congruent, meaning they have the same length. Let's add this information to our diagram.

Now we can add the four side lengths to find the perimeter. Perimeter: 57+ 41+ 57+ 41=196 The parallelogram has the perimeter of 196 inches.

We want to find the area and perimeter of the given figure. Let's start by identifying our figure!

Our figure is a polygon with three angles and three sides. This means that our figure is a triangle. Now we can find the area and perimeter of the given triangle. Let's do it!

Area

Let's start by recalling the formula for the area of a triangle.

A=1/2bh In this formula, b is the length of the base and h is the height. Let's identify the base and height on our diagram!

For our triangle, we will substitute b= 56 for the base and h= 73 for the height into the formula to calculate A. Let's do it!
A=1/2bh
A=1/2( 56)( 73)
A=56/2* 73
A=28* 73
A=2044
The area of the triangle is 2044 square centimeters.

Perimeter

The perimeter of a figure is the sum of its side lengths. For a triangle, this is the sum of sides a, b, and c. P=a+b+c First,let's identify the side lengths on the given diagram.

To calculate P, we will substitute a= 73, b= 56, and c= 92 into the formula and simplify. Let's do it!
P=a+b+c
P= 73+ 56+ 92
P=221
The perimeter of the triangle is 221 centimeters.

Extra

Learn More!

More information about the area and perimeter of shapes can be found in our original courses! Please note that clicking on this link will navigate away from this page.

Perimeter and Area in a Coordinate Plane