Understanding Areas of Triangles and Trapezoids: Key Concepts and Examples
This lesson covers the fundamental principles of calculating the areas of triangles and trapezoids. It demonstrates how to apply the area formulas: Area of a triangle (A = 1/2 * base * height) and area of a trapezoid (A = 1/2 * height * (base1 + base2)). Several examples illustrate finding areas of real-world shapes, including rectangles and parallelograms, showcasing when and how to use these formulas. Engage with practice problems designed to reinforce learning and ensure mastery of these essential geometry concepts.
Understanding Areas of Triangles and Trapezoids: Key Concepts and Examples
E N D
Presentation Transcript
10-2 Area of Triangles and Trapezoids Course 1 Warm Up Problem of the Day Lesson Presentation
Warm Up • Evaluate. • 1. If the height of a rectangle equals the base of a parallelogram and the base of the rectangle equals the height of the parallelogram, then the rectangle and the parallelogram have the same area. • 2. Find the area of a rectangle with a length of 53 in. and a width of 47 in. True 2,491 in2
Problem of the Day Which is a better deal, 3 discs for $5.00 or 4 discs for $7.00? 3/$5.00
You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram. Height Height Base Base
AREAOF A TRIANGLE The area A of a triangle is half the product of its base band its height h. 1 2 bh A = h b
Additional Example 1A: Finding the Area of a Triangle Find the area of the triangle. 1 2 bh A = Write the formula. 1 2 Substitute 20for b and 12for h. (20· 12) A = 1 2 Multiply. (240) A = A = 120 The area is 120 ft2.
Caution! The legs of a triangle must meet at a 90◦ angle in order to use their lengths as the base and height of the triangle.
Additional Example 1B: Finding the Area of a Triangle Find the area of the triangle. 1 2 bh A = Write the formula. 1 2 Substitute 30for b and 24for h. (30· 24) A = 1 2 Multiply. (720) A = A = 360 The area is 360 in2.
Check It Out: Example 1A Find the area of the triangle. 1 2 bh A = Write the formula. 1 2 Substitute 5for b and 8for h. (5· 8) A = 8 in. 1 2 5 in. Multiply. (40) A = A = 20 The area is 20 in2.
1 2 Substitute 4 for b and 24for h. (4 • 24) A = 1 2 1 1 2 2 Check It Out: Example 1B Find the area of the triangle. 1 2 bh A = Write the formula. 24 ft 1 2 Multiply. (108) A = A = 54 4 ft The area is 54 in2.
Additional Example 2: Application The diagram shows the section of a forest being studied. What is the area of the section? 1 2 bh A = Write the formula. 1 2 Substitute 43.9for b. Substitute 16for h. (43.9 •16) A = 1 2 Multiply. (702.4) A = A = 351.2 The area is 351.2 km2.
24.5 m 48 m Check It Out: Example 2 The diagram shows the section of a park being studied. What is the area of the section? 1 2 bh A = Write the formula. 1 2 Substitute 48for b. Substitute 24.5for h. (48· 24.5) A = 1 2 Multiply. (1176) A = A = 588 The area is 588 m2.
AREAOF A TRAPEZOID b2 The area of a trapezoid is the product of half its height and the sum of its bases. 1 2 h(b1 + b2) A = h b1
1 2 Substitute 4 for h, 14 for b1, and 12 for b2. · 4(14 + 12 ) A = 1 2 · 4(26 ) 1 1 A = 2 2 1 2 Additional Example 3: Finding the Area of a Trapezoid Find the area of the trapezoid. 1 2 h(b1 + b2) Use the formula. A = A = 53 Multiply. The area is 53 yd2.
Check It Out: Example 3 12 cm Find the area of the trapezoid. 7 cm 16 cm 1 2 h(b1 + b2) Use the formula. A = 1 2 Substitute 7 for h, 16 for b1, and 12 for b2. · 7(16 + 12) A = 1 2 · 7(28) A = A = 98 Multiply. The area is 98 cm2.
Lesson Quiz Find the area of each triangle. 1. 3. 84 mi2 39.9 cm2 2. Find the area of each trapezoid. 3 4 22.5 m2 4. 113 in2
