The triangle inscribed within square ABCD has, as its base, side AD, and has a height of 6 cm. If the area of the triangle is 21 cm2, what is the area of the shaded region?
Oh, triangles and squares, the best shapes to play hide and seek in! I hope the shading doesn't make them camera shy. Now, let me get to the answer while having some fun.
Since the triangle has a base of side AD, we know that AD is equal to the base of the triangle. If the height of the triangle is 6 cm, we can use the formula for the area of a triangle, which is 1/2 times base times height.
So, plugging in the values, we get 21 = 1/2 * AD * 6. To find AD, we can solve the equation:
21 = 3 * AD.
Thus, AD = 7 cm. Since the triangle is inscribed within the square ABCD, the triangle divides the square into two equal right-angled triangles, whose combined areas equal the area of the square.
Therefore, the area of the shaded region, which is one of the right-angled triangles, is half the area of the square. So, we need to find the area of the square to calculate the shaded area.
Since AD is 7 cm, the side of the square is also 7 cm. The area of a square is given by s^2, where s is the side length.
Thus, the area of the square is 7^2 = 49 cm^2.
Finally, the area of the shaded region, which is half the area of the square, is 49/2 = 24.5 cm^2. Voila, we found the answer, along with some geometry jokes along the way!
To find the area of the shaded region, we need to subtract the area of the triangle from the area of the square.
The area of a triangle is given by the formula:
Area = (base * height) / 2
In this case, the base of the triangle is equal to the length of side AD of the square, and the height is given as 6 cm.
So, using the formula, we can find the base of the triangle:
Area = (base * 6) / 2
21 = (base * 6) / 2
To solve for the base, we can multiply both sides by 2 and divide by 6:
42 = base
Now that we know the base of the triangle is 42 cm, we can find the area of the square. Since the base of the triangle is equal to side AD of the square, we know that the side length of the square is also 42 cm.
The area of a square is given by the formula:
Area = side length^2
So, the area of the square is:
Area = 42^2
Area = 1764 cm2
Finally, to find the area of the shaded region, we subtract the area of the triangle from the area of the square:
Shaded area = Area of square - Area of triangle
Shaded area = 1764 cm2 - 21 cm2
Shaded area = 1743 cm2
Therefore, the area of the shaded region is 1743 cm2.
What shaded region?
The triangle inside the square has an area of 21cm. The shaded area is the remaining space outside the triangle inside the square.
if the triangle base is the side s,
6s/2 = 21
s = 7
area of square = 49
49-21=28