1. Mr. Peter Richard P.R Find the Area and Perimeter of
Perimeter and Area of Triangles, Quadrilaterals, and Trapezoids
P.R
Find the Area and Perimeter of
Quadrilaterals, Triangles, and Trapezoids.
Mr. Peter Richard
Will make sure you don’t get trapped
in a Trapezoid made by
some Square Triangle.
Algebra 1

2. Additional Example 1: Finding the Perimeter of Triangles and Trapezoids
Find the perimeter of each figure. A. 7
Add all sides. 4
P = 10
= 21 units 17 8 11 6
Add all sides. B.
P =
= 42 units

3. AREA OF A TRIANGLE Words Numbers Formula
Triangle: The area A of a triangle is one-half the base length b times the height h.
A = (8)(4)
= 16 units2 Think of a Triangle as half of a Rectangle
1 2

4. Triangle Area = ½ bh ( ‘h’ is the vertical height)
b b

5. Area of Parallelograms
Height –
* The altitude of the //-ogram.
* Line from a vertex of the //-ogram  to the opposite side.
Base – Is any of its sides.
A = bh
Area of a //-ogram
* units 2
Height
Base

6. Example 1: Find the area of the following //-ogram.
A = bh
= (12m)(8m)
= 96m2
Perimeter?
= 45m

7. A triangle or trapezoid can be thought of as half of a parallelogram.

8. AREA OF A TRAPEZOID Words Numbers Formula
Trapezoid: The area is ½ times the height h times the sum of the bases (b1 +b2)
Bases = two Parallel Sides
A = (h)(b1 + b2)
1 2
A = (2)(3 + 7)
= 10 units2
1 2

9. Additional Example 2A: Finding the Area of Triangles and Trapezoids
Graph and find the area of the figure with the given vertices.
A. (–2, 2), (4, 2), (0, 5)
Area of a triangle y
A = bh 1 2
(0, 5)
Substitute for b and h.
= • 6 • 3 1 2 3
(–2, 2)
(4, 2) 6
= 9 units2 x

10. Additional Example 2B: Finding the Area of Triangles and Trapezoids
Graph and find the area of the figure with the given vertices.
B. (–1, 2), (5, –2), (5, 2), (–1, 6) y
(–1, 6)
Area of a trapezoid
A = h(b1 + b2) 1 2
(5, 2)
Substitute for h, b1, and b2. 8 6 4 x
= • 6(8 + 4) 1 2
(–1, –2)
(5, –2)
= 36 units2

11. Graph and find the area of the figure with the given vertices.
Try This: Example 2A
Graph and find the area of the figure with the given vertices.
A. (–1, 1), (1, 7), (7, 1)
Area of a triangle y
(1, 7)
A = bh 1 2
Substitute for b and h. 6
= • 8 • 6 1 2
(7, 1)
(–1, 1)
= 24 units2 x 8

12. Graph and find the area of the figure with the given vertices.
Try This: Example 2B
Graph and find the area of the figure with the given vertices.
B. (–2, –1), (0, 5), (3, 5), (5, –1) y
Area of a trapezoid 3 7 6
(3, 5)
(0, 5)
A = h(b1 + b2) 1 2
Substitute for h, b1, and b2. x
= • 6(7 + 3) 1 2
(–2, –1)
(5, –1)
= 30 units2

13. Find the shaded area Area of square = 10 x 10 = 100 cm2 10cm
A. of triangle = ½ x 3 x 4
= 6 cm2
Shaded area = 100 – 6
= 94 cm2
10cm
3cm
3cm
4cm

14. Problem #19
The tree farm needs fertilizing. Each box of fertilizer covers 36 square feet. About how many boxes of fertilizer are needed?

15. Because the path is 1 ft wide, increase each side
Margaret’s garden is a square 12 ft on each side. Margaret wants a path 1 ft wide around the entire garden. What will the outside perimeter of the path be?
Because the path is 1 ft wide, increase each side
of the garden by 1 ft. s = = 14
P = 4s Formula for perimeter of a square
P = 4(14) = 56 Substitute 14 for s.
The perimeter is 56 ft.
1-7

16. 1. Find the perimeter in inches.
2. Find the area in square feet.
3. How many bags of fertilizer would cover the area if each bag covers 2 Sq. FT?
4. Find the perimeter of a triangle whose vertices
are X(–6, 2), Y(8, 2), and Z(3, 14).
5. Find the area of the figure below. All angles are right angles.
A rectangle is 9 ft long and 40 in. wide.
296 in.
30 ft2
81 cm2
42 units
256 in.2 PR

17. Lesson Homework
Use the figure to find the following measurements.
1. The perimeter of the triangle
36 cm
2. The perimeter of the trapezoid
44 cm
3. The perimeter of the combined figure
64 cm
4. The area of the triangle
54 cm2
5. The area of the trapezoid
104 cm2