Question

find the area of the quadrilateral ABCD , in which AC = 36 cm. BL and DM perpendiculars from B and D to AC are 16 cm and 18 cm respectively .​

Answer 1

Answer:

★ see the fig.

Area of quadrilateral ABCD

⟹ Area ( Δ ABC ) + Area ( Δ ADC)

⟹ ½ × AC × BL + ½ × AC × DM

⟹ ½ AC×(BL+DM)= [½×36×(16+18)]cm²

⟹ ( 18 × 34 ) cm²

⟹ 612 cm²

Hence, the area of the quadrilateral ABCD is 612cm²

Answer 2

Answer:   Area of the quadrilateral  ABCD  = 612 $cm^{2}$

Explanation:

Given - ABCD quadrilateral area

            AC = 36cm.

             BL = 16cm.

             DM = 18cm.

Find - Area of the quadrilateral ABCD = ?

∵ Area of the ABCD = Area of the Δ ABC +  Area of the ΔADC

• Formula of the tringle = $\frac{1}{2}$ × $Base$ × $Height$

∴  Area of the ABCD = Area of the Δ ABC +  Area of the ΔADC

                                  = $\frac{1}{2}$ × AC × BL + $\frac{1}{2}$ × AC × DM

                                  = $\frac{1}{2}$ × 36 × 16 + $\frac{1}{2}$ × 36 × 18

                                   = $\frac{1}{2}$ × 36 ( 16 + 18 )   → (take $\frac{1}{2}$  and 36 common )

                                    = 18 × (34 )

  Area of the ABCD  = 612 $cm^{2}$