8-4 area of triangles and trapezoids learn to find the area of triangles and trapezoids
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8-4 Area of Triangles and Trapezoids
Learn to find the area of triangles and trapezoids.
8-4 Area of Triangles and Trapezoids
You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.
8-4 Area of Triangles and Trapezoids
8-4 Area of Triangles and Trapezoids
Find the area of the triangle.
Additional Example 1A: Finding the Area of a Triangle
A = 12
bh Write the formula.
A = 12
(20 · 12) Substitute 20 for b and 12 for h.
A = 120
The area is 120 ft2.
A = 12
(240) Multiply.
8-4 Area of Triangles and Trapezoids
An altitude of a triangle is a perpendicular segment from one vertex to the line containing the opposite side. The length of the altitude is the height.
Reading Math
8-4 Area of Triangles and Trapezoids
Find the area of the triangle.
Additional Example 1B: Finding the Area of a Triangle
A = 12
bh Write the formula.
A = 12
(30 · 24) Substitute 30 for b and 24 for h.
A = 360
The area is 360 in2.
A = 12
(720) Multiply.
8-4 Area of Triangles and Trapezoids
Find the area of the triangle.
Check It Out: Example 1A
A = 12
bh Write the formula.
A = 12
(5 · 8) Substitute 5 for b and 8 for h.
A = 20
The area is 20 in2.
A = 12
(40) Multiply.
8 in.
5 in.
8-4 Area of Triangles and Trapezoids
Find the area of the triangle.
Check It Out: Example 1B
A = 12
bh Write the formula.
A = 54
The area is 54 in2.
A = 12
(108) Multiply.
24 ft
4 ft12
A = 12
(4 • 24)12
Substitute 4 for b and 24 for h.
12
8-4 Area of Triangles and Trapezoids
The diagram shows the section of a forest being studied. What is the area of the section?
Additional Example 2: Application
A = 12
bh Write the formula.
A = 12
(43.9 • 16) Substitute 43.9 for b. Substitute 16 for h.
A = 351.2
The area is 351.2 km2.
A = 12
(702.4) Multiply.
8-4 Area of Triangles and Trapezoids
The diagram shows the section of a park being studied. What is the area of the section?
Check It Out: Example 2
A = 12
bh Write the formula.
A = 12
(48 · 24.5) Substitute 48 for b. Substitute 24.5 for h.
A = 588
The area is 588 m2.
A = 12
(1176) Multiply.
24.5 m
48 m
8-4 Area of Triangles and Trapezoids
8-4 Area of Triangles and Trapezoids
Find the area of the trapezoid.
Additional Example 3: Finding the Area of a Trapezoid
A = 12
h(b1 + b2) Use the formula.
A = 53
The area is 53 yd2.
Multiply.
A =12
· 4(26 )12
Substitute 4 for h, 14 for b1, and 12 for b2.
12
A = 12
· 4(14 + 12 )12
8-4 Area of Triangles and Trapezoids
Find the area of the trapezoid.
Check It Out: Example 3
A = 12
h(b1 + b2) Use the formula.
A = 12
· 7(16 + 12)
A =12
· 7(28)
A = 98
The area is 98 cm2.
Substitute 7 for h, 16 for b1, and 12 for b2.
Multiply.
12 cm
16 cm
7 cm