ABCD rectangle with AB = 8 cm, BC = 16 cm and AE = 4 cm. Find the area

1.	ABCD rectangle with AB = 8 cm, BC = 16 cm and AE = 4 cm. Find the area of ABCE. Is the area of ΔBEC equal to the sum of the area of ΔBAE and ΔCDE. Why?
Answer» Given : In rectangle ABCD, AB = 8cm, BC = 16 cm, AE = 4cm Now Area of ΔBAE = 12 x base x height = 1/2 x \(\overline {BC} \times \overline {AB}\) = 1/2 × 16 x 8 = 64cm² = 1/2 × 16 x 8 = 64cm² = 1/2 x \(\overline {ED} \times \overline {DC}\) = 1/2 × 12 × 8 = 48cm² ⁽\(\overline {ED}\) = AD – AE = 16 – 4 = 12cm and \( \overline {DC} = \overline {AB}\)) Now ΔBAE + ΔCDE = 16 + 48 = 64 = ΔBCE.

ABCD rectangle with AB = 8 cm, BC = 16 cm and AE = 4 cm. Find the area of ABCE. Is the area of ΔBEC equal to the sum of the area of ΔBAE and ΔCDE. Why?

Answer»

Given : In rectangle ABCD,

AB = 8cm, BC = 16 cm, AE = 4cm

Now Area of ΔBAE = 12 x base x height

= 1/2 x \(\overline {BC} \times \overline {AB}\)

= 1/2 × 16 x 8 = 64cm²

= 1/2 x \(\overline {ED} \times \overline {DC}\)

= 1/2 × 12 × 8 = 48cm²

⁽\(\overline {ED}\) = AD – AE = 16 – 4 = 12cm and \( \overline {DC} = \overline {AB}\))

Now ΔBAE + ΔCDE = 16 + 48 = 64 = ΔBCE.