Square ABCD and triangle APB lie on same base AB. If area of square is 16 cm square find ar (triangle ABP) where P is a point on side CD.
well the area of a triangle is 1/2 the area of a rectangle with same base and height.
To find the area of triangle ABP, we need to determine the length of the base (AB) and the height (the distance from point P to side AB).
First, let's determine the length of side AB. We are given that the area of the square is 16 cm². The area of a square is equal to the side length squared. So, by taking the square root of the area, we can find the length of side AB.
√(Area of Square) = √16 cm² = 4 cm
Now, let's consider the height or the distance from point P to side AB. Since point P is on side CD of the square, the height of the triangle is perpendicular to side AB. Let's call the height h.
In a square, the diagonals bisect each other at 90-degree angles, so line AD is perpendicular to line CD. Therefore, triangle ADP is a right triangle with a base of length AD and a height of length h.
Since the area of the square is 16 cm², each side of the square is 4 cm. As triangle ADP is a right triangle, we can use the Pythagorean theorem to find the height:
AD² + DP² = AP²
4² + DP² = AP²
16 + DP² = AP²
Now, the length of AD is the same as the side length of the square, which is 4 cm. So, we have:
16 + DP² = AP²
Next, we can determine the length of DP. Since P is a point on side CD, it means that DP is the remaining length from P to the edge of the square. Since each side of the square is 4 cm, DP = 4 - x, where x represents the horizontal distance from P to the edge of the square.
Now, substituting DP with 4 - x in the equation:
16 + (4 - x)² = AP²
16 + 16 - 8x + x² = AP²
32 - 8x + x² = AP²
Since we don't have any information about x, we cannot simplify further. Therefore, the area of triangle ABP cannot be determined without more specific information.