Express the area of ABCD in terms of the measurements k and d. Chapter 11 10 Glencoe Geometry. TILINGS Tile making often requires an artist to find clever ways of dividing a shape into several smaller, congruent shapes. FRAMING A rectangular poster measures 42 inches by 26 inches. Trapezoid ABCD ~ trapezoid EFGH. The area of the trapezoid is 435 square meters. Chapter 11 Resource Masters.
13 cm ALGEBRA Find x. If she cuts each circle into three congruent pieces, what is the area of each piece? The measure of central angle RAS is 360 5 or 72. Highlight the interior of the parallelogram using the Selection Arrow tool from the toolbar.
CUTOUTS A trapezoid is cut from a 6-inch-by-2-inch rectangle. The area is 336 square meters. Find the area of the walkway to the nearest tenth. Area of a Circle If a circle has an area of A square units and a radius of r units, then A = πr 2. Construct a segment by selecting the Segment tool from the toolbar. Area of rectangle = (3 ft)(7 ft) = 21 ft 2 Area of trapezoid = 1 (6 ft)(10 ft + 3 ft) = 39 ft2 2 Area of composite figure A = 21 ft 2 + 39 ft 2 = 60 ft 2. 11-1 skills practice areas of parallelograms and triangles answers. 4 Multiply each side by 10. 26 So, A = 1 2 ap = 1 2 ( 60) (8. The logo consists of two triangles that have the dimensions shown. Composite figure A is similar to composite figure B. Do you see any patterns or relationships?
FOUNTAIN A local park has two fountains in the shape of similar trapezoids as shown. X Length of arc = 2(π)(r) 360 Length of AB = 100 2(π)(6) x = 100 and r = 6 360 10. The sum of the areas of the basic figures is the area of the figure. 11-3 Enrichment Perimeter of a Sector You have learned how to find the area of a sector of a circle using a ratio of the circle and the area formula.
5 cm A = 240 cm 2 Chapter 11 36 Glencoe Geometry. What is the area of the nonagon? 29 cm Lesson 11-2 16 m ALGEBRA Find each missing length. SANDWICHES For a party, Samantha wants to have finger sandwiches. V R A P S T Example 1 Verify the formula A = 1 ap for the regular pentagon above. 11 1 skills practice areas of parallelograms and triangles practice. 10 ft Step 1: Find the area of composite figure A. POOL A circular pool is surrounded by a circular sidewalk. 7 Use this scale factor to find the value of x. CD HJ = k x 10 = 8 7 The ratio of corresponding lengths of similar polygons is equal to the scale factor between the polygons.
So the area of the 2 pentagon is A = 5 ( 1 (RS)(AP). 100 Exercises 2(6) + 10. 11-5 Study Guide and Intervention Areas of Similar Figures Areas of Similar Figures If two polygons are similar, then their areas are proportional to the square of the scale factor between them. 11-3 Practice Areas of Circles and Sectors Find the area of each circle. 11 1 skills practice areas of parallelograms and triangle.ens. Construct a parallel line to the second segment by highlighting the second segment and the point not on it. Find the length of each diagonal. Next, construct a point on the intersection of the two lines. 18 mm 10 mm 12 mm 4 ft 60 5. Find the area of PQR. 5 The perimeter of the sector is about 22. The area of a circle is 201.
C. Suppose the wall is marked where the poster will hang. 18 ft 24 ft 24 ft 7. Explain your answer. A trapezoid has base lengths of 19. Make the appropriate changes in Steps 1 3 above to inscribe a regular pentagon in P. Answer each of the following. 11-1 Study Guide and Intervention (continued) Areas of Parallelograms and Triangles Areas Of Triangles The area of a triangle is one half the product of the base and its corresponding height. TRACK A running track has an inner and outer edge. In terms of r, what is the area of the black region? The diameter of the circle is 15 feet. Multiply the ratio of the degree measure of the intercepted arc to 360 by the circumference of the circle. Thus, its base is k times as large as that of trapezoid I and its height its k times as large as that of trapezoid I. side of trapezoid II side of trapezoid I = ks 2 s 2 = k b 1 kb 1 s 1 h s2 ks 1 kh ks 2 perimeter trapezoid II perimeter trapezoid I = k(s 1 + s 2 + b 1 + b 2) s 1 + s 2 + b 1 + b 2 = k b 2 kb 2 Trapezoid I Trapezoid II Perimeter = s 1 + s 2 + b 1 + b 2 Perimeter = ks 1 + ks 2 + kb 1 + kb 2 = k (s 1 + s 2 + b 1 + b 2) Solve. 17 cm 40 cm 15 cm 25 cm 20 in. Substitution x = 8 10 or 11.
5 cm A = 200 cm 2 4. Show how to divide the trapezoid into 4 congruent trapezoids. 7 m Find the area of each figure. 5 ft 12 ft ALGEBRA Find each missing length. 11-1 Study Guide and Intervention Areas of Parallelograms and Triangles Areas of Parallelograms Any side of a parallelogram can be called a base. The base of a triangle is four times its height. The area of the shaded region is (10)(30) - 3π(5 2) = 300-75π 64. The larger pin has a side length that is three times longer than the smaller pin. If the clock face has a diameter of 20 centimeters and is divided into congruent pieces so that each sector is 30, what is the area of each piece? What are the perimeter and area of each triangle? If the scale factor is 1:20, what is the area of his model? 11-5 Enrichment Areas of Similar Figures You have learned that to find the area of a composite figure, you find the area of each basic figure and then use the Area Addition Postulate.
A trapezoid has base lengths of 6 and 15 centimeters with an area of 136. The length of the smaller poster is 6 inches. The cakes consist of two geometrically similar shapes as shown. 12 m p The area of the circle is about 113. P sector = 2r + length of AB 6 in. A = lw - 1 2 πr2 = 50(30) - 0. Does this measurement match the one found by the Geometer s Sketchpad? Press CLEAR so the pointer becomes a black arrow. The radii of the inner edge semicircles are 25 yards each and the radii of the outer edge 100 yd 25 yd semicircles are 32 yards each.