Solve the following problem using what you know about composite figures. What is the area of the figure
An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top and bottom on the left side
To find the area of the figure, we need to find the area of the entire polygon and subtract the area of the missing rectangular piece.
The entire polygon can be divided into three rectangles.
The first rectangle has a length of 6 and a width of 2, which gives us an area of 6 * 2 = 12.
The second rectangle has a length of 6 and a width of 4 (the remaining width after subtracting the missing rectangular piece width), which gives us an area of 6 * 4 = 24.
The third rectangle has a length of 6 and a width of 2, which gives us an area of 6 * 2 = 12.
The total area of the entire polygon is 12 + 24 + 12 = 48.
The missing rectangular piece has a length of 6 and a width of 2, which gives us an area of 6 * 2 = 12.
Therefore, the area of the figure is 48 - 12 = 36.
The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
A composite figure is comprised of a rectangle and two congruent right triangle on both sides. The triangles have a height of 4 inches and a width of 3 inches.
Let's call the length of the rectangle within the composite shape as 'x'.
The area of the two congruent right triangles is (1/2) * base * height for each triangle, which is (1/2) * 3 * 4 = 6 square inches for each triangle. Therefore, the total area of both triangles is 2 * 6 = 12 square inches.
The remaining area of the composite shape, after subtracting the area of the triangles, is 40 - 12 = 28 square inches.
Since the remaining area is a rectangle, its area is equal to its length multiplied by its width. So, we need to solve for 'x' in the equation 'x * y = 28', where 'y' is the width of the rectangle.
Since we do not have the value for 'y', we are unable to determine the specific area of the rectangle within the composite shape with the information provided.
Solve the following problem: A town has a swimming pool shaped as in the diagram.
What is the area of the swimming pool in square yards?
A composite shape is drawn with a rectangle and a square. All lines are straight and all corners are marked as right angles. The shape is made with a vertically aligned rectangle 8 yards in length and 7 yards in width. A horizontally aligned rectangle 3 yards wide and of unknown length is removed from the bottom left corner of the original rectangle. The remaining width along the bottom right is 3 yards.
To find the area of the swimming pool, we need to find the area of the original rectangle and subtract the area of the rectangle that was removed.
The original rectangle has a length of 8 yards and a width of 7 yards, so its area is 8 * 7 = 56 square yards.
The rectangle that was removed has a width of 3 yards and an unknown length. Let's call the length of the removed rectangle 'x' yards. The remaining width along the bottom right is 3 yards.
To find the length of the removed rectangle, we can set up the following equation: 7 - 3 - 3 = x. This simplifies to 1 = x.
So, the length of the removed rectangle is 1 yard.
The area of the removed rectangle is 3 * 1 = 3 square yards.
Therefore, the area of the swimming pool is 56 - 3 = 53 square yards.
these are the options: 56 square yards
56 square yards
44 square yards
44 square yards
65 square yards
65 square yards
30 square yards
My apologies for the mistake. The correct answer is 56 square yards.
show why
To find the area of the swimming pool, we need to calculate the area of the original rectangle and subtract the area of the rectangle that was removed.
The original rectangle has a length of 8 yards and a width of 7 yards. The area of a rectangle is calculated by multiplying its length and width, so the area of the original rectangle is 8 * 7 = 56 square yards.
The rectangle that was removed has a width of 3 yards and a length of 1 yard. The area of a rectangle is calculated by multiplying its length and width, so the area of the removed rectangle is 3 * 1 = 3 square yards.
To find the area of the swimming pool, we subtract the area of the removed rectangle from the area of the original rectangle: 56 - 3 = 53 square yards.
Therefore, the correct answer is that the area of the swimming pool is 53 square yards.
John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?
A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.