Question

Find the area of quadrilateral ABCD from the given measurements in the figure below. AB is perpendicular to BC and AE is perpendicular to CD.​

Answer 1

Answer:

In Triangle ABC

• AB perpendicular BC
• Base = BC = 8 cm
• Height = AB = 15 cm

Area of Triangle ABC = 1/2 x Base x Height

• 1/2 x BC x AB
• 1/2 x 8 x 15
• 4 x 15
• 60 cm²

In Triangle ABC

By Pythagoras theorm : AC² = AB² + CB²

• AC² = 15² + 8²
• AC² = 225 + 64
• AC² = 289
• AC = 17 cm

In Triangle AEC

• AE perpendicular CE
• Height = AE = 6 cm

By Pythagoras theorm : AC² = AE ² + CE²

• 17² = 6² + CE²
• CE² = 17² - 6²
• CE² = 289 - 36
• CE² = 253
• CE = 15.9 cm

Area Triangle AEC = 1/2 x base x height

• 1/2 x CE x AE
• 1/2 x 15.9 x 6
• 15.9 x 3
• 47.7 cm²

In Triangle AED

• AE perpendicular ED
• Base = ED = CD-CE = 21-15.9 = 5.1 cm
• Height = AE = 6 cm

Area of Triangle AED = 1/2 base x height

• 1/2 x ED x AE
• 1/2 x 5.1 x 6
• 5.1 x 3
• 15.3 cm²

Area of Quadrilateral ABCD

• Area of Triangle ABC + Area of Triangle AED + Area of Triangle AEC
• 60 + 15.3 + 47.7 cm²
• 123 cm²

Answer = 123 cm²