holt ca course 1 10-4 area of triangles and trapezoids warm up california standards lesson...
DESCRIPTION
Holt CA Course Area of Triangles and Trapezoids AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d – the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered: AF1.2, AF3.2 California Standards 1212TRANSCRIPT
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
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Holt CA Course 1
10-4 Area of Triangles and Trapezoids
Warm UpEvaluate.
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12 · 6 · 812 · 5.4 · 7.2
3. 4(7 + 10)4. 3.5(12 + 8.2)
1.
70.7
2.
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d – the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).Also covered: AF1.2, AF3.2
California Standards
1 2
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
The two parallel sides of a trapezoid are its bases, b1 and b2. The height of a trapezoid is the perpendicular distance between the bases.
h
b1
b2
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
In the term b1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.”
Reading Math
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
A. Find the area of the triangle.
Additional Example 1: Finding the Area of a Triangle
5
8
A = 12 bh Use the formula.
A = 12 (8 · 5) Substitute 8 for b and 5 for h.
A = 20
The area of the triangle is 20 square units.
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
A. Find the area of the trapezoid.
Additional Example 2: Finding the Area of a Trapezoid
5 in.
6 in.
9 in.
A = 12
h(b1 + b2) Use the formula.
A = 12
· 6(9 + 5)
A =12 · 6(14)
A = 42
The area of the trapezoid is 42 in2.
Substitute.
Multiply.
Add.
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state?
Additional Example 3: Geometry Application
A = 12
h(b1 + b2) Use the formula.
A = 12
· 300(153 + 220)
A =12 · 300(373)
A = 55,950
The area of Wisconsin is approximately 56,000 square miles.
Substitute.
Multiply.
Add.
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
B. Find the area of the triangle.
A = 12 bh Use the formula.
A = 12 (7 · 10) Substitute 7 for b and 10 for h.
A = 35
The area of the triangle is 35 square units.
Check It Out! Example 1
10
7
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
A. Find the area of the trapezoid.
A = 12
h(b1 + b2) Use the formula.A = 1
2· 6(11 + 4)
A =12 · 6(15)
A = 45
The area of the trapezoid is 45 in2.
Substitute.
Multiply.
Add.
Check It Out! Example 2
4 in.6 in.
11 in.
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
A large preserve has a similar trapezoid shape. What is the approximate area of the preserve?
Check It Out! Example 3
232 mi
116 mi
A = 12
h(b1 + b2) Use the formula.
A = 12
· 129(232 + 116)
A =12 · 129(348)
A = 22,446
The area of the preserve is approximately 22,446 square miles.
Substitute.
Multiply.
Add.
129 mi
Holt CA Course 1
10-4 Area of Triangles and TrapezoidsLesson Quiz
Find the area of each figure.
1.
3.
9 in245 ft2
60 ft2 87.5 ft2
2.
4.
4. What is the height of a triangle with area 36 cm2 and a base 9 cm? 8 cm
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
A. Find the area of the triangle.
A = 12 bh Use the formula.
A = 12 (6 · 9) Substitute 6 for b and 9 for h.
A = 27
The area of the triangle is 27 square units.
Check It Out! Example 1
6
9
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
B. Find the area of the triangle.
Additional Example 1: Finding the Area of a Triangle
9A = 12bh Use the formula.
A = 12 (12 · 9) Substitute 12 for b and 9 for h.
A = 54
The area of the triangle is 54 square units.
12
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
B. Find the area of the trapezoid.
Additional Example 2: Finding the Area of a Trapezoid
A = 12
h(b1 + b2) Use the formula.
A = 12
· 7(16 + 12)
A =12 · 7(28)
A = 98
The area of the trapezoid is 98 cm2.
Substitute.
Multiply.
Add.
12 cm
16 cm
7 cm
Holt CA Course 1
10-4 Area of Triangles and Trapezoids
B. Find the area of the trapezoid.
A = 12
h(b1 + b2) Use the formula.A = 1
2· 9(5 + 16)
A =12 · 9(21)
A = 94.5
The area of the trapezoid is 94.5 cm2.
Substitute.
Multiply.
Add.
Check It Out! Example 2
16 cm
5 cm
9 cm