Find the perimeter and area of quadrilateral ABCD in which AB = 9 cm, AD = 12 cm, BD = 15 cm, CD = 17 cm and ∠CBD = 90°.
Mensuration
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Question

Find the perimeter and area of quadrilateral ABCD in which AB = 9 cm, AD = 12 cm, BD = 15 cm, CD = 17 cm and ∠CBD = 90 .

KnowledgeBoat · Accepted Answer

Given, AB = 9 cm AD = 12 cm BD = 15 cm CD = 17 cm ∠CBD = 90 Diagonal BD divides the quadrilateral into two triangles: △ABD and △BCD. For △ABD, Sides are 9 cm, 12 cm, 15 cm. Since, 92 + 122 = 81 + 144 = 225 = 152. So they are the pythagorean triplets. So triangle △ABD is a right angled triangle. Area of right angle triangle = × Base × Height Area of triangle ABD = × AB × AD = × 9 × 12 = 9 × 6 = 54 cm2. For △BCD, Since, ∠CBD = 90 ∴ Applying Pythagoras theorem for the △BCD, ⇒ BD2 + BC2 = DC2 ⇒ 152 + BC2 = 172 ⇒ BC2 = 289 - 225 ⇒ BC2 = 64 ⇒ BC = ⇒ BC = 8 cm. Area of △BCD = × BC × BD = × 8 × 15 = 4 × 15 = 60 cm2. Area of quadrilateral △ABCD = Area of △ABD + Area of △BCD = 54 + 60 = 114 cm2. Perimeter of quadrilateral ABCD = AB + BC + CD + DA = 9 + 8 + 17 + 12 = 46 cm. Hence, area = 114 cm2 and perimeter = 46 cm.

Mathematics

Find the perimeter and area of quadrilateral ABCD in which AB = 9 cm, AD = 12 cm, BD = 15 cm, CD = 17 cm and ∠CBD = 90°.

Mensuration

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