Core Connections: Course 2
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2. Section 1.2
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Exercise 141 Page 61

Practice makes perfect

We want to find the area and perimeter of the given rectangle. We can do these things one at a time.

Area

We will start by recalling the formula for calculating the area of a rectangle. A=l w Now let's consider the given diagram. We will substitute l= 12 and w= 8 into the formula to calculate A. Let's do it!
A=l w
A= 12( 8)
A=96
The area of the rectangle is 96 square centimeters.

Perimeter

In general, the perimeter of a figure is the sum of its side lengths. A rectangle has two pairs of equal sides, so we can find its perimeter using the following formula. P=2l+2w In this formula, l is the length and w is the width. We already determined that l= 12 and w= 8, so let's substitute these values into our formula and simplify.
P=2l+2w
P=2( 12)+2( 8)
P=24+16
P=40
The perimeter of the rectangle is 40 centimeters.

Let's find the area and perimeter of the given triangle.

Area

Now we can find the area of a triangle using the following formula to do it. A=1/2bh In this formula, b is the length of the base and h is the height. Let's look at our diagram! For our triangle, we will substitute b= 11 for the base and h= 4 for the height into the formula to calculate A. Let's do it!
A=1/2bh
A=1/2( 11)( 4)
A=11/2* 4
A=5.5* 4
A=22
The area of the triangle is 22 square inches.

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 We can calculate P if we substitute the given values a= 5, b= 11, and c= 9.05 into the formula and simplify. Let's do it!
P=a+b+c
P= 5+ 11+ 9.05
P=25.05
The perimeter of the triangle is 25.05 inches.

Next, let's find the area and perimeter of the given parallelogram.

Area

The area of a parallelogram is the product of its base and its height. A=bh Let's identify the base and the height of the parallelogram on the given diagram!

In the given parallelogram, the base is 16 centimeters and its corresponding height is 9 centimeters. Let's substitute these values into the formula for the area of a parallelogram and simplify.
A=bh
A= 16( 9)
A=144
The area of the parallelogram is 144 square centimeters.

Perimeter

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

We can see that the parallelogram has two side lengths of 16 centimeters and two side lengths of 10 centimeters. Let's add the four side lengths to find the perimeter. Perimeter: 16+ 10+ 16+ 10=52 The parallelogram has the perimeter of 52 centimeters.

Finally, we want to find the area and the perimeter of the given trapezoid.

Area

The area of a trapezoid is half of its height times the sum of the lengths of its bases. A=1/2h(b_1+b_2) Let's identify the bases and height of the trapezoid on the given diagram!

In the given trapezoid, the bases are 25 and 44.67 meters and the height is 20 meters. Let's substitute these values into our formula and simplify.
A=1/2h(b_1+b_2)
A=1/2( 20)( 25+ 44.67)
A=1/2(20)(69.67)
A=20/2(69.67)
A=10(69.67)
A=696.7
The area of the trapezoid is 696.7 square meters.

Perimeter

We want to calculate the perimeter of the trapezoid. We can start by marking the side lengths of the figure.

The perimeter of a trapezoid is calculated by adding its four side lengths. Let's calculate the perimeter! Perimeter: 25+ 44.67+ 21+ 24=114.67 The trapezoid has a perimeter of 114.67 meters.