✨ First of all we find the area of the rectangle .
☃️ Area of rectangle = (24 × 15) cm²
→ Area of rectangle = 360 cm² .
✴️ It is clearly that,
✔️ Area of the shaded region = Area of the rectangle - [Area of (∆ADF + ∆ABE + ∆CEF)]
(i) Area of ∆ADF ;-
☃️ Area of ∆ADF = 1/2 × AD × DF
→ Area of ∆ADF = 1/2 × 15 × 12
→ Area of ∆ADF = 15 × 6
→ Area of ∆ADF = 90 cm²
(ii) Area of ∆ABE ;-
☃️ Area of ∆ABE = 1/2 × AB × BE
→ Area of ∆ABE = 1/2 × 24 × 7
→ Area of ∆ABE = 12 × 7
→ Area of ∆ABE = 72 cm²
(iii) Area of ∆CEF ;-
☃️ Area of ∆CEF = 1/2 × CE × CF
→ Area of ∆CEF = 1/2 × 8 × 12
→ Area of ∆CEF = 4 × 12
→ Area of ∆CEF = 48 cm²
⚡ Therefore,
Area of the shaded region = 360 - (90 + 72 + 48)
→ Area of the shaded region = 360 - 210
→ Area of the shaded region = 150 cm²
∴ The area of the shaded region is '150cm²' .
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Answers & Comments
✨ First of all we find the area of the rectangle .
☃️ Area of rectangle = (24 × 15) cm²
→ Area of rectangle = 360 cm² .
✴️ It is clearly that,
✔️ Area of the shaded region = Area of the rectangle - [Area of (∆ADF + ∆ABE + ∆CEF)]
(i) Area of ∆ADF ;-
☃️ Area of ∆ADF = 1/2 × AD × DF
→ Area of ∆ADF = 1/2 × 15 × 12
→ Area of ∆ADF = 15 × 6
→ Area of ∆ADF = 90 cm²
(ii) Area of ∆ABE ;-
☃️ Area of ∆ABE = 1/2 × AB × BE
→ Area of ∆ABE = 1/2 × 24 × 7
→ Area of ∆ABE = 12 × 7
→ Area of ∆ABE = 72 cm²
(iii) Area of ∆CEF ;-
☃️ Area of ∆CEF = 1/2 × CE × CF
→ Area of ∆CEF = 1/2 × 8 × 12
→ Area of ∆CEF = 4 × 12
→ Area of ∆CEF = 48 cm²
⚡ Therefore,
Area of the shaded region = 360 - (90 + 72 + 48)
→ Area of the shaded region = 360 - 210
→ Area of the shaded region = 150 cm²
∴ The area of the shaded region is '150cm²' .