Transcript 2D3D-L1 Perimeter and Area of 2D Shapes

20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Perimeter and Area
of 2D Shapes
2D3D-L1 Objectives:
To perform routine applied mathematics operations
correctly on a scientific calculator.
Learning Outcome B-4
Slide 1
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Perimeter is the total length around the outside of a closed geometric
figure. To find the perimeter of a polygon, such as a rectangle, you add
the lengths of all sides of the figure. If the figure is circular, you find its
circumference.
Theory – Perimeter
Slide 2
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
The following formulas can be used to calculate the perimeter of
geometric figures. You do not have to memorize the formulas for these
specific cases. The perimeter of a triangle is simply the sum of the length
of the three sides.
Triangles
a)Scalene: P = a + b + c
(no sides the same length)
(b) Isosceles: P = 2a + b
(two sides the same length)
c) Equilateral: P = 3a
(all sides the same length)
Theory – Perimeter of a Triangle
Slide 3
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
The perimeter of four-sided figures (quadrilaterals) can be calculated by
finding the sum of the four sides. In some special cases the sides have
the same length and an abbreviated formula is possible though not
necessary.
(a) General: P = a + b + c + d
(b) Trapezoid: P = a + b + c + d
(c) Parallelogram: P = 2a + 2b
(d) Rectangle: P = 2l + 2w
(e) Square: P = 4s
(f) Rhombus: P = 4a
Theory – Perimeter of a
Quadrilateral
Slide 4
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
The perimeters of pentagons, hexagons, and other polygons are
calculated in the same way – add together the lengths of all sides of the
figure.
The perimeter of a circle is called its circumference. The circumference
is found by using a formula:
C = 2πr or C = πd , where r is the radius and d is the diameter. These
formulae are essentially the same as 2r = d.
Theory – Perimeter of a
Quadrilateral
Slide 5
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Example 1
(a) Find the perimeter of Δ ACB.
(b) Find the perimeter of Δ ADB.
(c) Find the perimeter of quadrilateral ACBD.
Example 1
Slide 6
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Example 2
(a) Find the perimeter of the square ABCD.
(b) Find the circumference of the circle
with centre E.
Example 2
Slide 7
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
The area of a geometric figure is the amount of space that the 2D figure
covers. For example, you can find the area of the rectangle below by
counting the squares that are contained in the figure.
The rectangle covers eight squares or has an area of eight square units.
The algebraic model or formula that you can apply to calculate this area
is as follows:
A=lxw
= 4 units x 2 units
= 8 sq. units
Theory - Area
Slide 8
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
The formulas for finding the areas of other geometric figures are:
Anytime height (h) is used in a formula it must be measured
perpendicular to the base.
1. Triangles: A = ½bh
2. Trapezoid: A = ½(a + b)h, where a and b must be the parallel sides
3. Parallelogram: A = bh
4. Rectangle: A = lw
5. Square: A = s2
6. Rhombus: A = ah
7. Circle: A = πr2
Theory – Area of Geometric
Shapes
Slide 9
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
To find the areas of other more irregular shapes, break the figure into
one or more of the above shapes and add the resulting areas.
Example:
To find the area of the above figure, draw in the line segment AC. Find
the areas of the triangles ABC and ADC, and add the two areas.
Theory – Area of Irregularly
Shaped 2D Objects
Slide 10
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Example 3
Find the area of the triangle ABC
Example 3
Slide 11
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Example 4
Find the area of the shaded region.
Example 4
Slide 12
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Example 5
Find the area of the figure. (All angles are 900)
Example 5
Slide 13
20S Applied Math
Mr. Knight – Killarney School
Unit: Real Number System
Lesson: 2D3D-L1 Perimeter and Area of 2D Shapes
Example 6
Find the area of a uniform 1.2 m wide sidewalk around a flower garden
as shown in the figure. (The sidewalk is shaded.)
Example 6
Slide 14