Calculating Areas: Sector and Rectangle Problem Solving
In this guide, we explore how to calculate the area of various geometric figures, including circles and sectors. By applying the Area of a Sector Theorem, we demonstrate how to find the area of a sector when the total area and angle are known. We further discuss calculating areas involving rectangles and entrances composed of semicircles and squares. A series of examples and guided practices provide practical insights into these calculations, with corresponding answers to enhance understanding of area computation in geometry.
Calculating Areas: Sector and Rectangle Problem Solving
E N D
Presentation Transcript
315 = Area ofV Solve for Area of V. The area of Vis 315 square meters. mTU Area of sectorTVU = Area ofV 360° 40° 35 = Area ofV ANSWER 360° Use the Area of a Sector Theorem EXAMPLE 3 Use the diagram to find the area of V. SOLUTION Write formula for area of a sector. Substitute.
Standardized Test Practice EXAMPLE 4 SOLUTION The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.
180° = 36(26) – (π 82 ) + 162 360° ANSWER The correct answer is C. Standardized Test Practice EXAMPLE 4 = 936 – [32π+ 256] ≈ 579.47 The area is about 579square feet.
4. Find the area of H. ANSWER about 907.92 cm2 for Examples 3 and 4 GUIDED PRACTICE
5. Find the area of the figure. ANSWER about 43.74 m2 for Examples 3 and 4 GUIDED PRACTICE
ANSWER Yes; the formula for the area of sector is m π r2 A= and if you solve this for m, you get 360 360A . π r2 for Examples 3 and 4 GUIDED PRACTICE 6. If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain.
