Question

the dimensions of a rectangle ABCD are 51cm x 25cm. A trapezium PBCQ with parallel sides QC and PB in the ratio of 9:8 is cut off from the rectangle. If the area of the trapezium is 5 /6 part of the area of the rectangle find both the areas (35 points)

Answer 1

Now you can easily find the areas!

Answer 2

The area of the rectangle is 1275 $\text{cm}^{2}$ and the area of the trapezium is 1062.5 $\text{cm}^{2}$.

Step-by-step explanation:

We are given that the dimensions of a rectangle ABCD are 51 cm x 25 cm. A trapezium PBCQ with parallel sides QC and PB in the ratio of 9:8 is cut off from the rectangle.

Also, the area of the trapezium is (5/6) part of the area of the rectangle.

Let the length of the rectangle ABCD = L = 51 cm

and the breadth of the rectangle ABCD = B = 25 cm

The area of the rectangle ABCD is given by the following formula;

Area of a rectangle ABCD = Length of rectangle $\times$ Breadth of rectangle

                                            = 51 cm $\times$ 25 cm

                                            = 1275 $\text{cm}^{2}$

Now, it is stated that the area of the trapezium is (5/6) part of the area of the rectangle, that means;

Area of the trapezium  =  $\frac{5}{6} \times \text{Area of the rectangle}$

                                       =  $\frac{5}{6} \times 1275$

                                       =  $\frac{6375}{6}$  = 1062.5 $\text{cm}^{2}$.

Hence, the area of the rectangle is 1275 $\text{cm}^{2}$ and the area of the trapezium is 1062.5 $\text{cm}^{2}$.