To find the area of the polygon ABCDEF, we can divide it into smaller triangles and then calculate the area of each triangle.

Step 1: Divide the polygon into triangles
We can divide the polygon into three triangles: ADE, CFI, and BFG.

Step 2: Calculate the area of triangle ADE
Triangle ADE is a right triangle with AD as the base and AH as the height. The area of a triangle is given by the formula: Area = (base * height) / 2.

In this case, the base AD is given as 9 cm and the height AH is given as 4 cm. Therefore, the area of triangle ADE is (9 * 4) / 2 = 36 / 2 = 18 square cm.

Step 3: Calculate the area of triangle CFI
Triangle CFI is also a right triangle with CI as the base and AJ as the height. Using the same formula as above, the area of triangle CFI is (5 * 7) / 2 = 35 / 2 = 17.5 square cm.

Step 4: Calculate the area of triangle BFG
Triangle BFG is not a right triangle, so we cannot directly use the formula above. However, we can divide it into two right triangles: BFG and BFC.

Triangle BFG is a right triangle with BF as the base and BG as the height. Using the formula, the area of triangle BFG is (3 * 2) / 2 = 3 square cm.

Triangle BFC is a right triangle with FC as the base and FH as the height. Using the formula, the area of triangle BFC is (3 * 4) / 2 = 6 square cm.

Therefore, the total area of triangle BFG is 3 + 6 = 9 square cm.

Step 5: Calculate the total area of the polygon ABCDEF
To find the total area of the polygon, we sum up the areas of the triangles: ADE + CFI + BFG = 18 + 17.5 + 9 = 44.5 square cm.

Therefore, the area of the polygon ABCDEF is 44.5 square cm.

7.5 cm2
or
23.5cm2