Look at the figures below.
Figure A has 6 sides. The top side measures 6 feet, the shortest left side measures 3 feet, the shortest bottom side measures 3 feet, the right side measures 8 feet. Another bottom side and longest left side are unknown. The figure B is a right trapezoid with height 5 feet. The parallel sides measure 8 feet and 4 feet. A right triangle is separated by a dotted line. Figure C has a rectangle with length 7 feet and width 4 feet, and a triangle with height 5 feet is attached to the right of the rectangle. Figure D is a right trapezoid with height 2 feet. The parallel sides measure 8 feet and 7 feet. A right triangle is separate by a dotted line.
Sort the figures according to area. Drag each figure name from the Source list to the Target list to show the areas from LEAST to GREATEST.
Assuming the task is to sort the figures according to their areas, we need to calculate the areas of each figure first:
Figure A: To find the area of Figure A, we need to find the length of the missing sides. Since it is a hexagon, all sides are of equal length. Using the Pythagorean theorem, we can find the missing sides:
Using the given sides: 3^2 + 6^2 = 45
Taking the square root: √45 ≈ 6.71
Now we know that each side of Figure A is approximately 6.71 feet. The area of a regular hexagon is given by the formula: (3 * √3 * s^2) / 2, where s is the length of each side.
Area of Figure A: (3 * √3 * 6.71^2) / 2 ≈ 60.11 square feet
Figure B: The area of a trapezoid is given by the formula: ((a + b) * h) / 2, where a and b are the lengths of the parallel sides and h is the height.
Area of Figure B: ((8 + 4) * 5) / 2 = 30 square feet
Figure C: The area of a rectangle is given by the formula: length * width. The area of a triangle is given by the formula: (base * height) / 2.
Area of the rectangle in Figure C: 7 * 4 = 28 square feet
Area of the triangle in Figure C: (7 * 5) / 2 = 17.5 square feet
Total area of Figure C: 28 + 17.5 = 45.5 square feet
Figure D: The area of a trapezoid is given by the formula: ((a + b) * h) / 2, where a and b are the lengths of the parallel sides and h is the height.
Area of Figure D: ((8 + 7) * 2) / 2 = 15 square feet
Therefore, the figures should be sorted from LEAST to GREATEST area as follows:
Figure D (15 square feet) - Figure B (30 square feet) - Figure C (45.5 square feet) - Figure A (60.11 square feet)