Question

The length of the diagonal of a quadrilateral is 8 cm. The altitudes drawn on the diagonal from the other two vertices are 3 cm and 4 cm. Find the area of the quadrilateral?​

Answer 1

✬ Area = 28 cm² ✬

Step-by-step explanation:

Given:

• Length of diagonal of quadrilateral is 8 cm.
• Measure of two altitudes are 3 cm and 4 cm.

To Find:

• What is the area of quadrilateral ?

Solution: Let ABCD be a quadrilateral in which

• AC = 8 cm (diagonal)
• DE (3 cm) is altitude on AC.
• BF (4 cm) is altitude on AC.

Now, in ∆ADC

• AC = base , DE = height

★ Area = 1/2(Base)(Height) ★

➨ Area of ∆ADC = 1/2(8)(3)

➨ Area of ∆ADC = 12 cm²

Similarly, in ∆ABC

• AC = base , BF = Height

➨ Area of ∆ABC = 1/2(8)(4)

➨ Area of ∆ABC = 16 cm²

∴ Area of ABCD = ar.(ABC + ADC)

➟ Area of ABCD = (16 + 12) = 28 cm²

Hence, Area of quadrilateral is 28 cm².