b The sides with the same number of hatch marks have equal lengths.
A
aPerimeter: 28 feet
Area: 36 ft^2
B
bPerimeter: About 108 cm
Area: 600 cm^2
Practice makes perfect
a To find the perimeter of a shape, we have to add the length of its sides. Since we already know all of the shape's sides, we can find the perimeter directly.
P=2+5+10+11=28 feet
To find the area of the shape, we will first divide it into two right triangles.
To calculate the triangle's area, we need its base and height. From the diagram we see that these dimensions are already known, so we can find the shape's area by adding the triangles' areas.
1/2(2)(11)+1/2(5)(10)=36 feet^2
b Let's determine the perimeter and area one at a time.
Perimeter
Any side with the same number of hatch marks has the same length. With this information we can add some information to the diagram. We will also add a segment which will help us find the length of the unknown side.
One side remains unknown. This side is part of the right triangle's hypotenuse. Therefore, if we calculate this by the Pythagorean Theorem and subtracting 20 from it, we can determine this side.
The final side is (20sqrt(2)-20) cm. Let's add this information to the diagram.
With this information we can determine the shape's perimeter.
20+20+20+20+20+20sqrt(2)-20≈ 108 cm
Area
To find the area of the shape, we will divide it into a triangle and a rectangle.
To calculate the triangle's area we need its base and height, and to calculate the rectangle's area we need its width and length. From the diagram, we see that we have all of these dimensions and therefore, we can find the shape's area by adding these products.
(20)(20)+1/2(20)(20)=600 cm^2
