Calculate the shaded area of each of the following.
pls answer fast
Answers
Answer:
(AΔQPD)= 320cm²
A(ΔDYX)=80cm²
Step-by-step explanation:
Let the quadrilateral be ABCD.
A segment from point B to point D is the diagonal for the above quadrilateral.
Let the segment which is parallel to side AB be PQ.
Let the segment which is parallel to side BC be XY.
∴ In ΔDYX, angle DYX is 90° ...(Right angle)
∴ (DX)² = (DY)² + (XY)² ...( By Pythagoras Theorem)
∴ (DX)² = (10)² + (16)² ...(Given)
∴ (DX)² = 100+256
∴ (DX)² = 356
∴ DX = √356 ...(Taking square root on both sides)
∴ DX = 18.86 i.e. 19
∴ DX= 19cm
∴ In ΔQPD, angle P is 90° ...(Right angle)
∴ (QD)² = (QP)² + (PD)² ...(By Pythagoras Theorem)
∴ (QD)² = (20)² + (32)² ...(BC-16= 48-16=32)
∴ (QD)² = 400 + 1024
∴ (QD)² = 1424
∴ QD = √1424
∴ QD = 37.73 i.e. 38
∴QD = 38cm
∴ In ΔQPD,
A(ΔQPD) = ½ x base x height
∴ =½ x 32 x 20
∴ =½ x 640
∴(AΔQPD)= 320cm²
In ΔDYX,
A(ΔDYX) = ½ x base x height
∴ =½ x 16 x 10
∴ =½ x 160
∴A(ΔDYX)=80cm²
