280 likes | 291 Views
Learn how to find the perimeter and area of various figures, including triangles, trapezoids, parallelograms, and rhombi. Practice solving different math problems and improve your geometry skills.
E N D
A B C D Find the perimeter of the figure. Round to the nearest tenth if necessary. 48 cm 5-Minute Check 1
A B C D Find the perimeter of the figure. Round to the nearest tenth if necessary. 37.9 ft 5-Minute Check 2
A B C D Find the area of the figure. Round to the nearest tenth if necessary. 171.5 in2 5-Minute Check 3
A B C D Find the area of the figure. Round to the nearest tenth if necessary. 3.4 m2 5-Minute Check 4
A B C D Find the height and base of the parallelogram if the area is 168 square units. 12 units; 14 units 5-Minute Check 5
A B C D 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? 8.4 centimeters 5-Minute Check 6
Find areas of trapezoids. • Find areas of rhombi and kites. Then/Now
Area of a Trapezoid SHAVINGFind the area of steel used to make the side of the razor blade shown below. Area of a trapezoid h = 1, b1 = 3, b2 = 2.5 Simplify. Answer:A = 2.75 cm2 Example 1
A B C D Find the area of the side of the pool outlined below. 302.5 ft2 Example 1
OPEN ENDEDMiguel 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. Example 2
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. Example 2
Use the Pythagorean Theorem to find ℓ. a2 + b2 = c2 Pythagorean Theorem 42 + ℓ2 = 52 Substitution 16 + ℓ2 = 25 Simplify. ℓ2 = 9 Subtract 16 from each side. ℓ = 3 Take the positive square root of each side. Example 2
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. Example 2
The area of the trapezoid is the sum of the areas 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. Check Example 2
A B C D Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed. 88 ft2 Example 2
Area of a Rhombus and a Kite A. Find the area of the kite. Area of a kite d1 = 7 and d2 = 12 Answer: 42 ft2 Example 3A
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. Example 3B
Simplify. 2 Area of a Rhombus and a Kite Step 2 Find the area of the rhombus. Area of a rhombus d1 = 14 and d2 = 18 Answer: 126 in2 Example 3B
A B C D A. Find the area of the kite. 58.5 ft2 Example 3A
A B C D B. Find the area of the rhombus. 180 in2 Example 3B
1 __ 2 Step 1 Write an expression to represent each measure. Let x represent the length of one diagonal. Then the length of the other diagonal is x. 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? Example 4
Does the Rhombus Formula work for a Square? • s = 4 • d = ?
A = 64, d1= x, d2 = x 1 __ 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 Simplify. 256 = x2 Multiply each side by 4. 16 = x Take the positive square root of each side. Example 4
Answer: So, the lengths of the diagonals are 16 inches and (16) or 8 inches. 1 __ 2 Use Area to Find Missing Measures Example 4
A B C D Trapezoid QRST has an area of 210 square yards. Find the height of QRST. 6 yd Example 4