Area and Perimeter of Basic Geometric Shapes
Geometric shapes can be found in basic math classes. Teachers usually presents circles, rectangles, squares, triangles, and the like. Then we are asked to find the Area and Perimeters of such. Then what we missed always for the final answers are the units. In this page, we are presenting again some same basics of it. This might be easy for those who advanced but might helpful for those who is not really engage in math subjects or beginners. This can be the good page for review our basic geometrical information. Well, area is simply getting the entire plane of the object, while perimeter the addition of all sides of the said object. Let's go.
Illustrative Examples:
1. ) Find the Area and Perimeter of the given figure below.
Given: width (w) = 3 in.
length (l) = 5 in.
Required: Area and Perimeter
Solution: Area, taking all surface
Formula of Area of the rectangle: A = lw
A = lw
= 5 in. x 3 in. = 15 in. , answer
Solution: Perimeter, sum of all sides
Formula for the Perimeter of the rectangle: P = 2(l + w)
P = 2(5 in. + 3 in.)
= 2 ( 8 in.) = 16 in. , answer
2. ) Find the Area and Perimeter of the given figure below. So this is the same rectangle flipped side way. We can think which side will be our length or width, it doesn't matter.
We choose 7 cm. as our width, and 11 cm. for our length.
Given: width (w) = 7 cm.
length (l) = 11 cm.
Required: Area and Perimeter
Solution: Area, taking all surface
Formula of Area of the rectangle: A = lw
A = lw
= 7 cm. x 11 cm. = 77 cm. , answer
Solution: Perimeter, sum of all sides
Formula for the Perimeter of the rectangle: P = 2(l + w)
P = 2(11 cm. + 7 cm. )
= 2 ( 18 cm.) = 36 in. , answer
dimensions. If, just in case, the dimension is not given, we have to draw.
Figure 1.
In triangle, finding the slant side measurement needs special formula called Pythagorean Theorem, and the formula is found to be;
Where the c = hypotenuse side, a = adjacent side, and b= opposite side. See figure below. (see the theta for angle reference).
Figure 2.
So how to getting the slant side of the triangle in figure 2 is by the use of the said theorem, so we have;
Given a = 4
b = 1.5, (half of 3)
To solve for the value of c;
Now the dimension of the slant side.
To solve;
Base (b) = 3 ft.
Hypotenuse side = 4.27 ft.
Required: Area and Perimeter
Solution: Area, taking all surface
Formula for the Area of a triangle: A = 1/2(bh), (b = base, h =height)
A = 1/2(bh)
= 1/2(3 ft. x 4 ft.)
=1/2(7 sq. ft.), (sq = square, ft. feet)
= 3.5 square feet. , answer
Solution: Perimeter, sum of all sides
Formula for the Perimeter of a triangle: P = s1 + s2 +s3, (here, s1 = s2)
P = 4.27 ft. + 4.27 ft. + 3 ft.
= 11.54 ft. , answer
4. ) Find the Area and Circumference of the given circle below. We knew that circle has no perimeter, so we deal with the circumference instead.
Illustration:
So,
Radius (b) = 5 in., (r = diameter /2)
Required: Area and Circumference
Solution: Area, taking all surface
Formula for the Area of a circle:
or, if diameter is used;
Formula for the Circumference of a circle: for diameter
Example Problems:
1.) Given a rectangle with one side measures 10 in. and the other side 8 in., find the area and perimeter of the said object. (So we need to illustrate the statement).
Illustration:
Given: length (l) = 10 in.
width (w) = 8 in.
Required: Area and Circumference
Solution: Area, taking all surface
Formula for the Area of a rectangle: Area = l*w
Area = l*w
= 10 in. x 8 in.
= 80 sq. in. (sq. in = square inches), answer
Formula for the Perimeter of a rectangle: P = 2(l + w)
P = 2(l + w)
= 2 (10 in. + 8 in.)
= 2 (18 in.)
= 36 in., answer
2.) A triangle has the given dimension below, see figure.
Figure:
Given: Height (h) = 12 ft.
Base (b) = 9ft.
Required: Area and Perimeter
Solution: Area, taking all surface
Formula for the Area of a triangle: Area = 1/2 b*h
Area = 1/2 b*h
= 1/2 (9 ft.*12 ft.)
= 1/2 (108 sq. ft.)
= 54 sq. ft. , answer
We need to find the slant side(hypotenuse first before getting the Perimeter
Formula for the Perimeter of a triangle:
P = S1 +S2 +S3
P = 9 ft. + 12 ft. + 15 ft.
P = 36 ft., answer
3.) A circle has radius measures 7 cm. Find its area and Circumference. (So we need to illustrate the statement).
Illustration:
Required: Area and Circumference
Solution: Area, taking all surface
Formula:
Circumference Formula:
So we have to illustrate the figure knowing it is not visually given.
Illustration:
Required: Area and Perimeter
Solution: Area, taking all surface
Let's take a pop Quiz:
1.) Find the Area and the perimeter of the given figure below.
Illustration:
Perimeter is: click to write your answer
2.) What is the Area and Perimeter of the given triangle below?
Area is: click to write your answer
Perimeter is: click to write your answer
3.) Find the Area and Circumference of the circle whose radius measures 4 inches.
"here you have to illustrate the statement"
Quiz:
1.) The top of the table measures 4 ft. by 6 ft. .What is the area of the table and its Perimeter?
"here you have to illustrate the statement"
Area is: ___________or click
Perimeter is: ___________or click
2.) Given the figure below, find its Area and Perimeter.
figure:
Perimeter is: ___________or click
3.) The standard size of a Basket ball ring is 18 inches in diameter. Find its Area and Circumference.
"here you have to illustrate the statement"
Circumference is: ___________or click
4.) Find the total Area and Perimeter of the given figure below.
Figure:
Perimeter is: _________ or click
5.) Find the total Area of the given figure below.
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