Lesson Menu FiveMinute Check over Lesson 10 1

Lesson Menu Five-Minute Check (over Lesson 10– 1) Mathematical Practices Then/Now New Vocabulary Key Concept: Area of a Trapezoid Example 1: Real-World Example: Area of a Trapezoid Example 2: Area of a Trapezoid Key Concept: Area of a Rhumbus or Kite Example 3: Area of a Rhombus and a Kite Example 4: Use Area to Find Missing Measures Concept Summary: Areas of Polygons

Over Lesson 10– 1 Find the perimeter of the figure. Round to the nearest tenth if necessary. A. 48 cm B. 56 cm C. 101. 1 cm D. 110 cm

Over Lesson 10– 1 Find the perimeter of the figure. Round to the nearest tenth if necessary. A. 37. 9 ft B. 40 ft C. 43. 9 ft D. 45 ft

Over Lesson 10– 1 Find the area of the figure. Round to the nearest tenth if necessary. A. 58 in 2 B. 83 in 2 C. 171. 5 in 2 D. 180 in 2

Over Lesson 10– 1 Find the area of the figure. Round to the nearest tenth if necessary. A. 9. 0 m 2 B. 62 m 2 C. 5 m 2 D. 3. 4 m 2

Over Lesson 10– 1 Find the height and base of the parallelogram if the area is 168 square units. A. 11 units; 13 units B. 12 units; 14 units C. 13 units; 15 units D. 14 units; 16 units

Over Lesson 10– 1 The area of an obtuse triangle is 52. 92 square centimeters. The base of the triangle is 12. 6 centimeters. What is the height of the triangle? A. 2. 1 centimeters B. 4. 2 centimeters C. 8. 4 centimeters D. 16. 8 centimeters

Mathematical Practices 1 Make sense of problems and persevere in solving them. 7 Look for and make use of structure. Content Standards G. MG. 3 Apply geometric methods to solve problems (e. g. , designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

You found areas of triangles and parallelograms. • Find areas of trapezoids. • Find areas of rhombi and kites.

• height of a trapezoid

Area of a Trapezoid SHAVING Find the area of steel used to make the razor blade shown below. Area of a trapezoid h = 1, b 1 = 3, b 2 = 2. 5 Simplify. Answer: A = 2. 75 cm 2

Find the area of the side of the pool outlined below. A. 288 ft 2 B. 295. 5 ft 2 C. 302. 5 ft 2 D. 310 ft 2

Area of a Trapezoid OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck. Read the Test Item You are given a trapezoid with one base measuring 4 feet, a height of 9 feet, and a third side measuring 5 feet. To find the area of the trapezoid, first find the measure of the other base.

Area of a Trapezoid Solve the Test Item Draw a segment to form a right triangle and a rectangle. The triangle has a hypotenuse of 5 feet and legs of ℓ and 4 feet. The rectangle has a length of 4 feet and a width of x feet.

Area of a Trapezoid Use the Pythagorean Theorem to find ℓ. a 2 + b 2 42 + ℓ 2 16 + ℓ 2 ℓ = = = c 2 52 25 9 3 Pythagorean Theorem Substitution Simplify. Subtract 16 from each side. Take the positive square root of each side.

Area of a Trapezoid By Segment Addition, ℓ + x = 9. So, 3 + x = 9 and x = 6. The width of the rectangle is also the measure of the second base of the trapezoid. Area of a trapezoid Substitution Simplify. Answer: So, the area of the deck is 30 square feet.

Area of a Trapezoid Check The area of the trapezoid is the sum of the areas of the right triangle and rectangle. The area of the triangle is or 6 square feet. The area of the rectangle is (4)(6) or 24 square feet. So, the area of the trapezoid is 6 + 24 or 30 square feet.

Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed. A. 58 ft 2 B. 63 ft 2 C. 76 ft 2 D. 88 ft 2

Area of a Rhombus and a Kite A. Find the area of the kite. Area of a kite d 1 = 7 and d 2 = 12 Answer: 42 ft 2

Area of a Rhombus and a Kite B. Find the area of the rhombus. Step 1 Find the length of each diagonal. Since the diagonals of a rhombus bisect each other, then the lengths of the diagonals are 7 + 7 or 14 in. and 9 + 9 or 18 in.

Area of a Rhombus and a Kite Step 2 Find the area of the rhombus. Area of a rhombus d 1 = 14 and d 2 = 18 2 Answer: 126 in 2 Simplify.

A. Find the area of the kite. A. 48. 75 ft 2 B. 58. 5 ft 2 C. 75. 25 ft 2 D. 117 ft 2

B. Find the area of the rhombus. A. 45 in 2 B. 90 in 2 C. 180 in 2 D. 360 in 2

Use Area to Find Missing Measures ALGEBRA One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64 square inches, what are the lengths of the diagonals? Step 1 Write an expression to represent each measure. Let x represent the length of one diagonal. Then the length of the other 1 x. diagonal is __ 2

Use Area to Find Missing Measures Step 2 Use the formula for the area of a rhombus to find x. Area of a rhombus 1 x A = 64, d 1= x, d 2 = __ 2 Simplify. 256 = x 2 16 = x Multiply each side by 4. Take the positive square root of each side.

Use Area to Find Missing Measures Answer: So, the lengths of the diagonals are 16 inches 1 (16) or 8 inches. and __ 2

Trapezoid QRST has an area of 210 square yards. Find the height of QRST. A. 3 yd B. 6 yd C. 2. 1 yd D. 7 yd