Q. 20

# The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

Answer :

**To Find:** Area of the parallelogram

**Given:** Adjacent sides of parallelogram ABCD: 34 cm and 20 cm

Length of the diagonal = 42 cm

**Concept Used:**

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

**Diagram:**

**Explanation:**

The diagonal of a parallelogram divides the parallelogram into two congruent triangles.

Therefore,

Area of Δ ADC = Area of Δ ABC

Let us calculate area of Δ ABC

s = 48 cm

Area = 4 × 6 × 7 × 2 cm^{2}

Area = 336 cm^{2}

Now, Area of parallelogram ABCD = 2 × 336 cm^{2}

**Hence, Area of parallelogram = 672 cm ^{2}.**

Rate this question :

A piece of land is in the shape of a rhombus ABCD in which each side measures 100m and diagonal AC is 160m long. Find the area of the rhombus.

RS Aggarwal & V Aggarwal - Mathematics

The question consists of two statements namely, Assertion (a) and Reason (R). Please select the correct answer.

The perimeter of an isosceles triangle is 32cm. The ratio of one of the equal side to its base is 3: 2. Find the area of the triangle.

RS Aggarwal & V Aggarwal - Mathematics