ABCD is a rectangle having length 40 cm and breadth 26 cm. P, Q, R, and S are the midpoints of AB, BC, CD, and AD respectively. If BD is the diagonal, what is the area (in c
m
2
) of the shaded part?
Answers
Answer:
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Given : ABCD is a rectangle having length 40 cm and breadth 26 cm. P, Q, R, and S are the midpoints of AB, BC, CD, and AD respectively
To find : what is the area of shaded part
Solution:
PQ² = PB² + BQ² = (AB/2)² + (BC/2)² = (40/2)² + (26/2)² = 20² + 13²
QR² = QC² + CR² = (BC/2)² + (CD/2)² = (26/2)² + (40/2)² = 13² + 20²
RS² = RD² + DS² = (CD/2)² + (DA/2)² = (40/2)² + (26/2)² = 20² + 13²
SP² = SA² + AP² = (DA/2)² + (AB/2)² = (26/2)² + (40/2)² = 13² + 20²
PQ² = QR² = RS² = PS²
=> PQ = QR = RS = PS
PQRS shaded area is a rhombus
diagonal are 40 cm & 26 cm
Area of rhombus = (1/2) * 40 * 26 = 520 cm²
Area of shaded area = 520 cm²
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