Question

In the figure quadrilateral abcd is a square of side 50m points p q r s are midpoints of sides ab bc CD and ad find area of shaded region

Answer 1

The area of shaded portion, given quadrilateral abcd is a square of side 50m points p q r s are midpoints of sides ab bc CD and ad is as follows.

Area of shaded portion = Area of square ABCD - Area of square PQRS

Given,

AB = BC = CD = DA = 50 M

AP = AS = AB/2 = 50/2 =25 M

PS² = AP² + AS²

= 25² + 25²

PS² = 1250

PS = 35.35 M

PS = SR = RQ = QP = 35.35 M

Area of square = a²  (a = side of the square)

Area of shaded portion = AB² - PS²

= 50² - 2 (25²)

= 2500 - 1250

= 1250 M²

Answer 2

1250 sq ,m

Step-by-step explanation:

By using following figure

Area of square ABCD = side × side = 50 × 50 = 2500 sq. m

P, Q, R, S are mid point of square ABCD

PB = ½ AB = ½ × 50 = 25 m

In ΔPBQ, ∠B = 90°

By Pythagoras theorem

$PQ^{2}$ = $PB^{2}$ + $PQ^{2}$

$PQ^{2}$ = $25^{2}$ + $25^{2}$

$PQ^{2}$ = 625 + 625

$PQ^{2}$ = 1250

Now area of square PQRS = $Side^{2}$ = $PQ^{2}$ = 1250 sq. m.

Area of  shaded region = Area of square ABCD – area of square PQRS

= 2500 – 1250

= 1250 sq ,m

To learn more

1)In a figure given below quadrilateral ABCD is a square of side 50 M. P Q R S are midpoints of sides ab and side BC sideCD and side AD respectively find the area of shaded region​

https://brainly.in/question/15965210