QuestionProve that two triangles, $\Delta$ and $\Delta$ , have equal area.

Studdy Solution

STEP 1

Assumptions1. The two triangles are denoted as $\Delta ABC$ and $\Delta DEF$ . . Both triangles have the same base length, denoted as $b$ .
3. Both triangles have the same height, denoted as $h$ .

STEP 2

The area of a triangle is given by the formula $Area = \frac{1}{2} \times base \times height$

STEP 3

Let's calculate the area of $\Delta ABC$ using the formula. $Area_{ABC} = \frac{1}{2} \times b \times h$

STEP 4

Now, let's calculate the area of $\Delta DEF$ using the same formula.
$Area_{DEF} = \frac{1}{2} \times b \times h$

STEP 5

Since both $Area_{ABC}$ and $Area_{DEF}$ are calculated using the same base and height, they are equal.
$Area_{ABC} = Area_{DEF}$ Therefore, we have proved that the two triangles $\Delta ABC$ and $\Delta DEF$ have the same area.

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