AND is an isosceles triangle while equal sides AB and AC are 10cm each and Base BC = 8cm. AD perpendicular to BC and angleBPC = 90°. Fund the area of shaded portion.
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Perpendicular drawn on side of isosceless triangle = AD
Thus, it will bisect the side BC.
= BD = CD = 8/2 =4 cm
In △ABD , Using the Pythagoras theorem
AB² = AD² + BD²
10² = AD² + 4²
100−16 = AD²
AD² = 84
AD = 2√21
In △PDB and △PDC
BD = CD (Proved)
PD = PD (Common)
∠PDB =∠PDC (Each 90°)
Thus, by SAS congruency c△PDB ≅ △PDC
In △PBC , Using Pythagoras theorem
PB² + PC² = BC²
PC² + PC² = 8²
2PC² = 64PC²
Pc = 4√2
In △ABC
= 1/2 × Base × Height
= 1/2 × BC × AD
= 1/2 × 8 × 2√21
= 8√21
Similarly,
Area of △PBC
= 1/2 × Base × Height
= 1/2 × PB × PC
= 1/2 × 4√2 × 4√2
= 16 cm²
Thus,
8√21 - 16
= 8 × 4.5 - 16
= 20.6cm²
Step-by-step explanation:
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