Construct trapezium PQRS where PQ is parallel to SR, PQ=7cm,Q=60°, QR=5cm and RS=4cm.Calculate its area.

the altitude is QR sin 60° = 5 * √3/2

So, the area is

A = (B+b)/2 * h = (4+7)/2 * 5/2 √3 = 55√3/4

To calculate the area of trapezium PQRS, we can use the formula:

Area = (1/2) * (sum of parallel sides) * (distance between the parallel sides)

First, let's calculate the length of side PS.

Since PQ is parallel to SR, we can see that angle QRS is also 60°.

Now, using the Law of Cosines, we can calculate side PS:

PS^2 = QR^2 + RS^2 – 2 * QR * RS * cos(QRS)
PS^2 = 5^2 + 4^2 – 2 * 5 * 4 * cos(60°)
PS^2 = 25 + 16 – 40 * 0.5
PS^2 = 25 + 16 – 20
PS^2 = 21

PS = √21

Now, we can calculate the area:

Area = (1/2) * (PQ + SR) * (PS)
Area = (1/2) * (7 + 4) * (√21)
Area = (1/2) * 11 * √21
Area = 11/2 * √21

Therefore, the area of trapezium PQRS is (11/2) * √21 cm^2.

To calculate the area of a trapezium, you need to follow these steps:

Step 1: Draw the trapezium PQRS according to the given dimensions. PQ is parallel to SR, PQ = 7 cm, Q = 60°, QR = 5 cm, and RS = 4 cm.

Step 2: Find the height of the trapezium. Draw a perpendicular line from point Q to SR, which is the base of the trapezium. Let's call the foot of the perpendicular T.

Step 3: To find the height QT, we need to use trigonometry. In triangle QTR, we have the angle Q = 60°, the adjacent side QR = 5 cm, and we need to find the opposite side QT (the height). Since the opposite side is the height, we can use the formula:

QT = QR * tan(Q)
= 5 * tan(60°)

By using a scientific calculator, we find that tan(60°) ≈ 1.732.

Therefore, QT ≈ 5 * 1.732 ≈ 8.66 cm

Step 4: Calculate the area using the formula for the area of a trapezium:

Area = ((PQ + SR) * height) / 2
= ((7 + 4) * 8.66) / 2
= (11 * 8.66) / 2
= 95.26 / 2
= 47.63 cm²

Therefore, the area of trapezium PQRS is approximately 47.63 cm².