the rectangle represented the AB side is 4cm the side BC is 6 cm i want to build a triangle taking the AB segment and the third vertice inside the triangle so his area becomes higher than 8 cm*cm.
the area in cm*cm of the region of the rectangle in which can be chosen the third vertice of the triangle is:
a) 12
b) 16
c) 8
d) 10
D----C
- -
- - 6cm
- -
A----B
4cm
To find the area of the region of the rectangle in which the third vertex of the triangle can be chosen to make its area greater than 8 cm², we need to consider the possible positions of the third vertex.
Since the rectangle is defined by two sides AB and BC, we can visualize the rectangle as follows:
D ───── C
│ │
│ │
│ │
A ───── B
Given that AB is 4 cm and BC is 6 cm, let's assume that the third vertex of the triangle can be positioned anywhere inside the rectangle except along AB and BC.
To calculate the area of the region where the third vertex can be chosen, we need to subtract the areas of the two triangles formed by placing the third vertex adjacent to AB and BC.
First, let's calculate the area of the rectangle, which is given by the formula length × width. In this case, it would be 4 cm × 6 cm = 24 cm².
Next, let's calculate the area of the triangle formed by placing the third vertex adjacent to AB. The height of this triangle is 4 cm, and its base would be equal to the length of BC, which is 6 cm. The area of this triangle is given by the formula ½ × base × height, which is equal to ½ × 6 cm × 4 cm = 12 cm².
Now, let's calculate the area of the triangle formed by placing the third vertex adjacent to BC. The height of this triangle is 6 cm, and its base would be equal to the length of AB, which is 4 cm. The area of this triangle is given by the formula ½ × base × height, which is equal to ½ × 4 cm × 6 cm = 12 cm².
To find the area of the region where the third vertex can be chosen, we subtract the areas of the two triangles from the area of the rectangle: 24 cm² - 12 cm² - 12 cm² = 0 cm².
Therefore, the area of the region in which the third vertex of the triangle can be chosen to make its area greater than 8 cm² is 0 cm².
So, none of the provided options (a, b, c, or d) are correct.