To find the value of ar(△ADE) + ar(△BCE), we need to use the given information that the area of parallelogram ABCD is 30cm².

Step 1: Draw a diagram of parallelogram ABCD and label the points A, B, C, and D.

Step 2: Identify the diagonals of the parallelogram. In this case, the diagonals are AD and BC.

Step 3: Divide the parallelogram into two triangles, △ADE and △BCE, by drawing a line segment from point A to point C.

Step 4: Calculate the area of the parallelogram ABCD. Since the area is given as 30cm², we have ar(ABCD) = 30cm².

Step 5: Use the property of parallelograms that opposite sides are equal in length and parallel to each other. This means that the base of triangle △ADE is equal to the base of triangle △BCE, which is the length of side AD.

Step 6: Let the length of side AD be 'x'. Therefore, the base of both triangles is 'x'.

Step 7: Use the formula for the area of a triangle, which is 1/2 * base * height. Since the base of both triangles is 'x', we can write the area of triangle △ADE as ar(△ADE) = 1/2 * x * height1, and the area of triangle △BCE as ar(△BCE) = 1/2 * x * height2.

Step 8: Since the height of both triangles is not given, we cannot directly calculate the areas of the triangles. However, we can use the fact that the area of the parallelogram is equal to the product of its base and height. Therefore, we have ar(ABCD) = x * height.

Step 9: Substitute the given area of the parallelogram (30cm²) into the equation from step 8: 30cm² = x * height.

Step 10: Solve the equation from step 9 for the height: height = 30cm² / x.

Step 11: Substitute the value of height into the equations for the areas of the triangles from step 7: ar(△ADE) = 1/2 * x * (30cm² / x) and ar(△BCE) = 1/2 * x * (30cm² / x).

Step 12: Simplify the equations from step 11: ar(△ADE) = 15cm² and ar(△BCE) = 15cm².

Step 13: Finally, calculate the sum of the areas of the triangles: ar(△ADE) + ar(△BCE) = 15cm² + 15cm² = 30cm².

Therefore, the value of ar(△ADE) + ar(△BCE) is equal to 30cm².

Question

To find the value of ar(△ADE) + ar(△BCE), we need to use the given information that the area of parallelogram ABCD is 30cm².

Step 1: Draw a diagram of parallelogram ABCD and label the points A, B, C, and D.

Step 2: Identify the diagonals of the parallelogram. In this case, the diagonals are AD and BC.

Step 3: Divide the parallelogram into two triangles, △ADE and △BCE, by drawing a line segment from point A to point C.

Step 4: Calculate the area of the parallelogram ABCD. Since the area is given as 30cm², we have ar(ABCD) = 30cm².

Step 5: Use the property of parallelograms that opposite sides are equal in length and parallel to each other. This means that the base of triangle △ADE is equal to the base of triangle △BCE, which is the length of side AD.

Step 6: Let the length of side AD be 'x'. Therefore, the base of both triangles is 'x'.

Step 7: Use the formula for the area of a triangle, which is 1/2 * base * height. Since the base of both triangles is 'x', we can write the area of triangle △ADE as ar(△ADE) = 1/2 * x * height1, and the area of triangle △BCE as ar(△BCE) = 1/2 * x * height2.

Step 8: Since the height of both triangles is not given, we cannot directly calculate the areas of the triangles. However, we can use the fact that the area of the parallelogram is equal to the product of its base and height. Therefore, we have ar(ABCD) = x * height.

Step 9: Substitute the given area of the parallelogram (30cm²) into the equation from step 8: 30cm² = x * height.

Step 10: Solve the equation from step 9 for the height: height = 30cm² / x.

Step 11: Substitute the value of height into the equations for the areas of the triangles from step 7: ar(△ADE) = 1/2 * x * (30cm² / x) and ar(△BCE) = 1/2 * x * (30cm² / x).

Step 12: Simplify the equations from step 11: ar(△ADE) = 15cm² and ar(△BCE) = 15cm².

Step 13: Finally, calculate the sum of the areas of the triangles: ar(△ADE) + ar(△BCE) = 15cm² + 15cm² = 30cm².

Therefore, the value of ar(△ADE) + ar(△BCE) is equal to 30cm².

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