Area of Trapezoids Goal Find the area of

Area of Trapezoids

Goal Find the area of trapezoids.

Key Vocabulary Trapezoid Base of a trapezoid Height of a trapezoid

Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Height of the trapezoid is the shortest distance (perpendicular distance) between the bases.

Area of Trapezoid b 1=base 1 h=height What is is the area of of this trapezoid? triangle? b 2=base 2

Area of Trapezoid b 1=base 1 h=height What is the area of this trapezoid? b 2=base 2 COPY THIS!

Area of Trapezoid b 1=base 1 h=height What is the area of this trapezoid? b 2=base 2 PASTE HERE!

Area of Trapezoid b 1=base 1 h=height What is the area of this trapezoid? b 2=base 2 FLIP VERTICALLY!

Area of Trapezoid b 1=base 1 h=height What is the area of this trapezoid? b 2=base 2 FLIP HORIZONTALLY!

Area of Trapezoid b 1=base 1 h=height What is the area of this trapezoid? b 2=base 2 TRANSLATE TO HERE!

Area of Trapezoid b 1=base 1 h=height What is the area of this trapezoid? b 2=base 2 b 1=base 1 CHECK MEASUREMENTS!

Area of Trapezoid b 1=base 1 Area of the trapezoid is ½ the area of this parallelogram? b 2=base 2 b 1=base 1 h=height

Area of Trapezoid b 1=base 1 h=height Area trapezoid = ½ height(base 1 + base 2) b 2=base 2 b 1=base 1

Area of Trapezoid b 1=base 1 h=height Area trapezoid = ½ h(b 1 + b 2) b 2=base 2 b 1=base 1

Area of Trapezoid Words: = ½(height)(base 1+base 2) Symbols: A = 1/2 h(b 1+b 2) Area

Example 1 Find the Area of a Trapezoid Find the area of the trapezoid. SOLUTION 1 A = h(b 1 + b 2) 2 1 = 2 (5)(6 + 8) 1 = 2 (5)(14) = 35 ANSWER Formula for the area of a triangle Substitute 5 for h, 6 for b 1, and 8 for b 2. Simplify within parentheses. Simplify. The area of the trapezoid is 35 square inches.

Video https: //www. youtube. com/watch? v=Bl 3 Flzb. If. E https: //www. youtube. com/watch? v=fy. OKq QKp. Ov. M Copyright Tim Morris/St Stephen's School

Your Turn: Find the area of the trapezoid. 1. ANSWER 63 m 2 ANSWER 182 ft 2 ANSWER 50 cm 2 2. 3.

What is the length of the missing side? bxh=A 20 x = 160 x = 80 m Plug in the stuff you know and solve for x!!

Area is 96 m 2. What is x?

If the area of this triangle is 21 square units, what is the length of x?

If the area of this triangle is 31. 5 square units, what is the length of x?

Area = 77 ft 2

Area is 39 square feet – what is b 1?

Example 2 Use the Area of a Trapezoid Find the value of b 2 given that the area of the trapezoid is 96 square meters. SOLUTION 1 A = h(b 1 + b 2) 2 1 96 = (8)(9 + b 2) 2 Formula for the area of a trapezoid Substitute 96 for A, 8 for h, and 9 for b 1. 192 = 8(9 + b 2) Multiply each side by 2. 192 = 72 + 8 b 2 Use the distributive property. 120 = 8 b 2 Subtract 72 from each side. 15 = b 2 ANSWER Divide each side by 8. The value of b 2 is 15 meters.

Your Turn: A gives the area of the trapezoid. Find the missing measure. 1. A = 77 ft 2 ANSWER h = 7 ft 2. A = 39 cm 2 ANSWER b 1 = 5 cm 3. A = 84 in. 2 ANSWER b 2 = 8 in. 4. A trapezoid has an area of 294 square yards. Its height is 14 yards and the length of one base is 30 yards. Find the length of the other base. ANSWER 12 yards