What is the area of shaded part in the diagram below given that PQRS is a rectangle PQ=12cm and QR =8cm?
Since PQRS is a rectangle, we know that opposite sides are congruent. So, QS must also be equal to 12cm.
To find the area of the shaded part, we need to subtract the area of the triangle QRS from the area of the rectangle PQRS.
The area of the triangle QRS can be found by using the formula for the area of a triangle: Area = 1/2 * base * height.
The base of the triangle is QR, which is 8cm.
The height of the triangle is QS, which is 12cm.
So, the area of the triangle QRS is 1/2 * 8cm * 12cm = 48cm^2.
The area of the rectangle PQRS is found by multiplying the length and width: Area = length * width = 12cm * 8cm = 96cm^2.
Therefore, the area of the shaded part is 96cm^2 - 48cm^2 = 48cm^2.
To calculate the area of the shaded part in the diagram, we need to subtract the area of the smaller rectangle from the area of the larger rectangle.
Let's start by calculating the area of the larger rectangle, PQRS.
Area of a rectangle = length x width
Area of PQRS = PQ x QR
PQ = 12 cm
QR = 8 cm
Area of PQRS = 12 cm x 8 cm = 96 cm²
Now, let's calculate the area of the smaller rectangle inside the larger rectangle.
Since both rectangles share the same width, the length of the smaller rectangle is equal to the difference between the length of the larger rectangle and the given dimension (6cm in this case).
Length of the smaller rectangle = PQ - 6 cm = 12 cm - 6 cm = 6 cm
Width of the smaller rectangle = QR = 8 cm
Area of the smaller rectangle = 6 cm x 8 cm = 48 cm²
Now we have the areas of both rectangles. To find the area of the shaded part, we subtract the area of the smaller rectangle from the area of the larger rectangle.
Area of the shaded part = Area of PQRS - Area of the smaller rectangle
Area of the shaded part = 96 cm² - 48 cm²
Area of the shaded part = 48 cm²
Therefore, the area of the shaded part in the diagram is 48 cm².
To find the area of the shaded part in the given diagram, we need to determine the area of the rectangle PQRS and subtract the sum of the areas of the two right triangles.
Step 1: Calculate the area of the rectangle PQRS.
The area of a rectangle is given by the formula: Area = Length x Width.
In this case, the length of the rectangle is PQ = 12 cm and the width is QR = 8 cm.
Therefore, the area of the rectangle PQRS is: Area = 12 cm x 8 cm = 96 cm².
Step 2: Calculate the area of the right triangles.
The area of a triangle is given by the formula: Area = (Base x Height) / 2.
In this case, both triangles have a base of QR = 8 cm.
Triangle 1:
To find the height of the first triangle, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's call the height of the triangle as h1.
Using the formula of the Pythagorean theorem, we have:
QR² = h1² + 8²
64 = h1² + 64
h1² = 64 - 64
h1² = 0
Therefore, h1 = 0.
Since the height of the first triangle is zero, the area of the triangle is also zero.
Triangle 2:
The second triangle is formed by the line segment SR, which is also the height of the rectangle. Therefore, the height of the second triangle, h2, is equal to the width of the rectangle, which is 12 cm.
Using the formula of the area of a triangle:
Area = (Base x Height) / 2 = (8 cm x 12 cm) / 2 = 48 cm².
Step 3: Subtract the sum of the areas of the triangles from the area of the rectangle.
Area of shaded part = Area of rectangle - (Area of triangle 1 + Area of triangle 2)
Area of shaded part = 96 cm² - (0 cm² + 48 cm²)
Area of shaded part = 96 cm² - 48 cm²
Area of shaded part = 48 cm².
Therefore, the area of the shaded part in the diagram is 48 cm².