Given a parallelogram ABCD, angle A = 60 degrees, AB = 10cm. Need to find Sabcd

To solve this task, we will supplement the drawing with one more construction;

Let us lower the height of BH from corner B to the side of AD and get a right-angled triangle ABH;

Since the angle A = 60 ° according to the condition of the assignment, then from the properties of the angles in the triangle we find the angle ABН, as;

AВН = 180 – (60 + 90) = 180 – 150 = 30 °;

From the property of a right-angled triangle, we know that the leg opposite to the angle of 30 ° is equal to half the hypotenuse, we write it down;

AH = 1/2 * 10 = 10/2 = 5cm;

By the Pythagorean theorem, we find the height of the ВН;

BH^2 = 10^2 – 5^2;

BH^2 = 100 – 25;

BH = √75;

BH = 5√3;

Find the area;

S = 5√3 * 12 = 60√3cm2.