A rectangular poster has a length of 72 centimeters and a width of 15 centimeters. The poster is reduced in size by 6 centimeters in length and 3 centimeters in width. What is the area of the new poster?(1 point)
A piece of paper is in the shape of a right triangle. The base is 4.25 inches and the height is 11 inches. What is the area of the right triangle in square inches?(1 point)
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An illustration shows a 10 by 10 grid. A non-right triangle is enclosed within the grid. The first vertex is at the top of row 2 and the right of column 6. The second vertex is at the top of row 8 and the right of column 1. The third vertex is at the top of row 10 and right of column 10.
What is the area of the non-right triangle? The base and height are found by counting the squares.
(1 point)
The area is
square units.
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An illustration shows a parallelogram with the right side as 16 inches. A perpendicular dotted line from top right vertex to the left side is 12 inches. The perpendicular line makes one right angle symbol with right side and two right angle symbols with the left side.
What is the area of the quadrilateral?
(1 point)
in.2
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An illustration shows the outline of letter upper H. The two vertical sides of the outline letter upper H have length 12 and width 3. The horizontal part across the middle has length 5. The inner side of the upper vertical part of the H has length 5. The inner side of the lower vertical part has length 6.
What is the area of the polygon?
(1 point)
Responses
72 square units
72 square units
83 square units
83 square units
77 square units
77 square units
68 square units
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An illustration of a parallelogram shows the following dimensions: The base is 12 feet. The perpendicular height from the top left vertex to the base is 7 inches. The height is drawn as a dashed line.
A pool company is installing a parallelogram-shaped swimming pool in a family’s back yard. Compose a rectangle to find the amount of area that the pool will take up in the yard. What is the area of the pool?
(1 point)
square feet
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An illustration shows an unfolded box net. It is comprised of a rectangle at the center, two squares extending into three trapezoids on the top and bottom, and a trapezoid on the left of the rectangle. The top side of the rectangle is labeled in three distinct sections: starting at the left, a solid line of 3 is drawn, followed by a dashed line of 3, and then a solid line of 6. The bottom of the rectangle is labeled in three distinct sections: a solid line of 6, a dashed line of 3, and a solid line of 3. The left width of the rectangle is drawn as a dashed line, labeled as 3, which becomes the base of a shaded trapezoid. The dashed lines on the top and bottom of the rectangle are extended into squares of side 3, sides drawn in dashed lines. The three outer sides of each square become the longer bases of shaded trapezoids. The top shorter side of the trapezoid is labeled as 1.2 and the perpendicular height is 1.
Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make the cube. Assume that all angles that look like right angles are right angles. All polygons that look congruent are congruent. What is the area of the shape in square inches?
(1 point)
square inches
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se the image to answer the question.
An illustration shows an outline of a right arrow consisting of a rectangle and a triangular head to its right. The length of the rectangle is 4 and the width is 2. The right width of the triangle does not show a line. It forms the central part of the verticle base of the triangle. The other parts of the base are labeled 2 on the top and bottom each. The perpendicular height from the base to the top vertex of the triangle is labeled as 5.
An artist is planning to paint an arrow using the pattern shown. What is the amount of area in square feet that will be painted?
(1 point)
square feet
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An illustration shows a rectangular prism. The top, front, and right faces are visible. The edges that are not visible are indicated by a dashed line. The base is labeled upper B equals 240 centimeters squared. The bottom front edge is labeled l equals 24 centimeters. A vertical edge is labeled h equals 8 centimeters.
Find the volume of the right rectangular prism.
(1 point)
cm3
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An illustration shows a vertical rectangular prism made of cubes placed as two columns, each 5 cubes high.
What is the volume of the right rectangular prism packed with 10 cubes? Each cube has an edge length of 13 meter.
(1 point)
Responses
1027 cubic meters
Start Fraction 10 over 27 End Fraction, cubic meters
127 cubic meters
, Start Fraction 1 over 27 End Fraction, cubic meters
10 cubic meters
, 10 cubic meters
103 cubic meters
, Start Fraction 10 over 3 End Fraction, cubic meters
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An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length is start fraction 1 over 2 end fraction, width is start fraction 1 over 4 end fraction, and height is start fraction 5 over 4 end fraction.
Multiply the edge lengths of a right rectangular prism with length 12 m, width 14 m, and height 54 m to show that the product is the same as the volume found by packing the prism with 10 unit cubes with an edge length of 14 m. What is the volume of the prism?
(1 point)
cubic meters
What is the volume of a rectangular prism with a length of 423 ft., a height of 313 ft., and a width of 212 ft.?(1 point)
ft.3
In cubic feet, what is the volume of a toy box measuring 334 feet long, 212 feet wide, and 212 feet tall? Use the volume formula to solve. The answer will be a mixed fraction in cubic feet.(1 point)
ft.3
Using the formula V=B×h, what is the volume of a rectangular prism with a length of 714 m, a width of 1012 m, and a height of 1225 m? The answer will be a mixed fraction in cubic meters.(1 point)
m3
1. The new poster has a length of 72 - 6 = 66 centimeters and a width of 15 - 3 = 12 centimeters. The area of the new poster is 66 x 12 = 792 square centimeters.
2. The area of the right triangle is (1/2) x 4.25 x 11 = 23.375 square inches.
3. To find the area of the non-right triangle, we need to find the length of the base and the height. The base has a length of (10 - 1) + (10 - 6) = 13. The height is the distance from the base to the vertex at the top of the triangle. To find the height, we can draw a perpendicular line from the top vertex to the base. This line has a length of 5. Therefore, the area of the triangle is (1/2) x 13 x 5 = 32.5 square units.
4. The area of a parallelogram is given by the formula A = base x height. In this case, the base is 16 inches and the height is 12 inches, so the area of the quadrilateral is 16 x 12 = 192 square inches.
5. To find the area of the polygon, we can split it up into two rectangles and two right triangles. The area of the two rectangles is (3 + 5 + 6) x 3 = 42. The area of the two right triangles is (1/2) x 3 x 5 + (1/2) x 6 x 3 = 9. Therefore, the area of the polygon is 42 + 9 = 51 square units.
6. To find the area of the parallelogram-shaped swimming pool, we can compose a rectangle with a length of 12 feet and a width of 7 inches (the perpendicular height). The area of this rectangle is 12 x 7 = 84 square feet.
7. To find the area of the shape, we need to decompose it into its component polygons. The rectangle has an area of 3 x 6 = 18 square inches. Each trapezoid has a height of 1 inch and an average of (3 + 6) / 2 = 4.5 for its two bases. Therefore, the area of each trapezoid is (1/2) x 1 x 4.5 = 2.25 square inches. There are two trapezoids, so their total area is 4.5 square inches. Finally, each square has an area of 3 x 1 = 3 square inches. There are two squares, so their total area is 6 square inches. Adding up all the areas gives a total of 18 + 4.5 + 6 = 28.5 square inches.
8. The area of the triangular head of the arrow is (1/2) x 2 x 5 = 5 square feet. The area of the rectangle is 4 x 2 = 8 square feet. Therefore, the total area of the painted arrow is 5 + 8 = 13 square feet.
9. The volume of the rectangular prism is given by the formula V = lwh. Plugging in the given values, we get V = 240 x 24 x 8 = 46,080 cubic centimeters.
10. The volume of the rectangular prism packed with 10 unit cubes is 10 x (13^3) = 27,950 cubic meters. The edge lengths of the original prism are 12 m, 14 m, and 54 m, so their product is 12 x 14 x 54 = 9,072 cubic meters. As expected, this is the same as the volume found using the unit cubes. Therefore, the volume of the original prism is 9,072 cubic meters.
11. Using the formula V = lwh, we get V = 423 x 313 x 212 = 29,267,964 cubic feet.
12. Using the formula V = lwh, we get V = 334 x 212 x 212 = 15,053,888 cubic feet. This simplifies to 14,999,000 + 54,888/3 cubic feet, or 14,999,000 and 2/3 cubic feet.
13. Using the formula V = Bh, we get V = 714 x 1012 x 1225 = 1,007,535,000 cubic meters. This simplifies to 937,500,000 + 70,035,000/3 cubic meters, or 937,500,000 and 23,345,000/3 cubic meters.