A trapezium measures 9.5cm (b1) 17cm (b2) & 6cm (h). Now, divide the trapezium into a rectangle & a triangle to find their areas. Hence, find the area of the trapezium.
To divide the trapezium into a rectangle and a triangle, we need to find the length of the rectangle's base.
The length of the rectangle's base (b) can be found by subtracting the length of the smaller base (b1) from the length of the larger base (b2):
b = b2 - b1
b = 17 cm - 9.5 cm
b = 7.5 cm
Now, we can find the area of the rectangle and the area of the triangle.
Area of the rectangle = length × width
Area of the rectangle = b × h
Area of the rectangle = 7.5 cm × 6 cm
Area of the rectangle = 45 cm²
Area of the triangle = (1/2) × base × height
Area of the triangle = (1/2) × b1 × h
Area of the triangle = (1/2) × 9.5 cm × 6 cm
Area of the triangle = 28.5 cm²
To find the area of the trapezium, we add the area of the rectangle and the area of the triangle:
Area of trapezium = area of rectangle + area of triangle
Area of trapezium = 45 cm² + 28.5 cm²
Area of trapezium = 73.5 cm²
Therefore, the area of the trapezium is 73.5 cm².
To find the area of the trapezium, we can divide it into a rectangle and a triangle. Let's calculate their areas step by step:
1. Rectangle:
The base of the rectangle is equal to the length of the trapezium's shorter parallel side (b1), which is 9.5cm.
The height of the rectangle is equal to the height of the trapezium (h), which is 6cm.
Therefore, the area of the rectangle is calculated as Area_rect = base × height = 9.5cm × 6cm.
2. Triangle:
The base of the triangle is equal to the difference between the lengths of the two bases of the trapezium (b2 - b1), which is 17cm - 9.5cm.
The height of the triangle is equal to the height of the trapezium (h), which is 6cm.
Therefore, the area of the triangle is calculated as Area_tri = (base × height) / 2 = [(17cm - 9.5cm) × 6cm] / 2.
3. Trapezium:
The area of the trapezium is the sum of the areas of the rectangle and the triangle.
Therefore, the total area of the trapezium is calculated as Area_trap = Area_rect + Area_tri.
Now, let's substitute the values and find the area of the trapezium:
Area_rect = 9.5cm × 6cm = ____ (calculate the value)
Area_tri = [(17cm - 9.5cm) × 6cm] / 2 = ____ (calculate the value)
Area_trap = Area_rect + Area_tri = ____ (add the calculated values of Area_rect and Area_tri)
By following these steps, you will be able to find the area of the trapezium.