3 The area of a triangle is $$ 10 \mathrm{~cm}^{2} $$. If the base of the triangle were increased by $$ 10 \% $$ and the height of the triangle were decreased by $$ 10 \% $$, what would be the area of the new resulting triangle?

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The area $$ A $$ of a triangle is given by the formula $$ A = \frac{1}{2} \times b \times h $$, where $$ b $$ is the base and $$ h $$ is the height. Given that the original area is $$ 10 \, \text{cm}^2 $$, we have:
Let the original base be $$ b $$ and the original height be $$ h $$. The new base after a $$ 10\% $$ increase is $$ b' = b + 0.1b = 1.1b $$. The new height after a $$ 10\% $$ decrease is $$ h' = h - 0.1h = 0.9h $$.
The area of the new triangle can be calculated using the new base and height:

$$
A' = \frac{1}{2} \times b' \times h' = \frac{1}{2} \times (1.1b) \times (0.9h)
$$

Substituting the original area $$ A = \frac{1}{2} \times b \times h = 10 \, \text{cm}^2 $$ into the equation, we can express the new area in terms of the original area.
Substituting the values, we have:

$$
A' = 1.1 \times 0.9 \times A = 0.99 \times 10 \, \text{cm}^2
$$
Calculate the value by following steps:
- step0: Calculate:
  $$0.99\times 10$$
- step1: Multiply the numbers:
  $$9.9$$
The area of the new triangle would be $$ 9.9 \, \text{cm}^2 $$.

3 The area of a triangle is . If the base of the
triangle were increased by and the height of the
triangle were decreased by , what would be the area
of the new resulting triangle?

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3 The area of a triangle is . If the base of the triangle were increased by and the height of the triangle were decreased by , what would be the area of the new resulting triangle?