Math, asked by Rajpoot5024, 7 months ago

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

Answered by rakshathsri
10

Answer:

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Answered by amitnrw
4

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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