Look at the figures below.

Question

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.

Answer 1

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)