If the length of the base of a triangle is increased by 10 percent and the height is decreased by 20 percent, what is the percent change (increase or decrease) in the area of the triangle?

To determine the percent change in the area of a triangle after the given modifications, we need to calculate the area before and after the changes, and then compare the two areas.

Let's assume the original base and height of the triangle are represented by B and H, respectively. The original area (A1) can be calculated as:

A1 = (1/2) * B * H

After increasing the base by 10 percent, the new base (B2) would be:

B2 = B + (10/100) * B
= B + 0.1B
= 1.1B

Similarly, after decreasing the height by 20 percent, the new height (H2) would be:

H2 = H - (20/100) * H
= H - 0.2H
= 0.8H

Now, we can calculate the new area (A2) using the modified base and height:

A2 = (1/2) * B2 * H2
= (1/2) * 1.1B * 0.8H
= 0.44B * 0.8H
= 0.352BH

To find the percentage change in the area, we need to calculate the difference between the new area (A2) and the original area (A1), and then express it as a percentage of A1:

Change in area = A2 - A1
= 0.352BH - (1/2)BH
= (0.352 - 0.5)BH
= -0.148BH

Now, to express this change as a percentage of the original area (A1), we divide the change by A1 and multiply by 100:

Percentage change = (Change in area / A1) * 100
= (-0.148BH / ((1/2)BH)) * 100
= -0.296 * 100
= -29.6

Therefore, the percent change in the area of the triangle is a decrease of 29.6 percent.

To find the percent change in the area of the triangle, we need to calculate the area before and after the changes in the base and height.

Let's assume the original base of the triangle was "b" units and the original height was "h" units. Therefore, the original area of the triangle can be calculated as:

Area = (1/2) * base * height = (1/2) * b * h

After increasing the length of the base by 10 percent, the new base will be 1.1 * b.
After decreasing the height by 20 percent, the new height will be 0.8 * h.

The new area of the triangle can be calculated as:

New Area = (1/2) * (1.1 * b) * (0.8 * h) = 0.44 * b * h

To find the percent change in the area, we can calculate the difference between the new area and the original area, and then express it as a percentage of the original area:

Change in Area = New Area - Original Area = 0.44 * b * h - (1/2) * b * h = 0.44 * b * h - 0.5 * b * h = -0.06 * b * h

Percent Change = (Change in Area / Original Area) * 100
= (-0.06 * b * h) / ((1/2) * b * h) * 100
= -0.12 * 100
= -12%

Therefore, there is a 12% decrease in the area of the triangle.

1.1 * 0.8 = 0.88

now you can get the change.