Unit 3, Lesson 9
Pongamos en práctica el área de los círculos
Grado 7
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Cada cuadrado tiene lados de 12 unidades de longitud. Compara las áreas de las regiones sombreadas de las 3 figuras. ¿Qué figura tiene la región sombreada más grande? Explica o muestra tu razonamiento.
Figure A of three equal sized figures labeled A B and C. Figure A is a square with a circle inside of it where the circle touches the midpoint of each side of the square. The regions outside of the circle are shaded blue.
Figure B of three equal sized figures labeled A B and C. Figure B is a square with four identical circles inside of it that do not overlap. The circles are arranged in two rows of two circles, are tangent to each other and tangent to the sides of the square. The area outside of the circles is shaded blue.
Figure C of three equal sized figures labeled A B and C. Figure C is a square with nine identical circles inside of it that do not overlap. The circles are arranged in three rows of three circles, are tangent to each other and to the sides of the square. The area outside of the circles is shaded blue.
Cada cuadrado de las figuras D y E tiene lados de 1 unidad de longitud. Compara el área de las dos figuras. ¿Cuál figura tiene más área?, ¿cuánta más? Explica o muestra tu razonamiento.
Figure D of two figures, labeled D and E. Figure D is composed of one square and two semi circles on top, and two bottom halves of circles and one square on the bottom. The top and bottom are divided by a horizontal dashed line.
Figure E of two figures, labeled D and E. Fiqure E is composed of 4 squares and 6 quarter circles. The 4 square are arranged diagonally, where the top right vertex of the first square is the same point as the bottom left vertex of the second square, the top right vertex of the second square is the same point as the bottom left vertex of the third square, and the top right vertex of the third square is the same point as the bottom left vertex of the fourth square. The corner circles align in between the sides of each square.
El campo que hay dentro de una pista de carreras está formado por un rectángulo de 84.39 m de largo y 73 m de ancho, junto con dos mitades de círculo en cada extremo. Los carriles de carrera tienen 9.76 m de ancho en todo el recorrido.
A picture of a field inside a running track. The field inside the track is composed of a rectangle, indicated by two dashed vertical lines labeled 73 meters and a horizontal length labeled 84 point 3 9 meters. There is a semi circle on each vertical side of the rectangle. The running track goes completely around the field and has a width of 9 point 7 6 meters.
¿Cuál es el área de la pista de carreras que está alrededor del campo? Explica o muestra tu razonamiento.
La relación que hay entre
Algunas veces, en lugar de dejar a
También podemos encontrar el área de una fracción de un círculo. Por ejemplo, esta figura muestra un círculo dividido en 3 partes que tienen la misma área. La parte sombreada tiene un área de
A circle divided into three equal sections. From the center of the circle three line segments extend to a point on the circle. The line segment extending downward and to the right is labeled “r”. The upper left region of the circle is shaded.