In the figure,
ABCD is a square with side 6 cm.
length(CE) 10 cm. Find the area of the shaded region
Answers
Answer:
24 sq.cm
Step-by-step explanation:
we have side CD=6cm and CE=10 cm
so by pythogoras theorem we can get DE=8cm
and shaded region is triangle we can find area of triangle by using the formula:1/2(Base-DE)(HEIGHT-CD) i.e. 1/2 bh
so after substituting the values we get answer 24sq cm
Area Of Shaded Region = 24 cm²
Step-by-step explanation:
GIVEN
Side = 6 cm
CE = 10 cm
___________________________
TO FIND
Area Of Shaded Region
___________________________
We know that,
Hypotenuse² = Base² + Height²
Here,
Hypotenuse = CE = 10 cm
Base = CD = 6 cm
Height = DE = ?
We know that,
Hypotenuse² = Base² + Height²
CE² = CD² + DE²
DE² = CE² - CD²
DE² = 10² - 6²
DE² = 100 - 36
DE² = 64
DE = √64
DE = 8
DE = 8 cm
___________________________
We know that,
Area Of Triangle = Area Of Shaded Region
Area Of Triangle = ½ × Base × Height
Here,
Base = 6 cm
Height = 8 cm
We know that,
Area Of Triangle = ½ × Base × Height
Area Of Triangle = ½ × 6 × 8
Area Of Triangle = ½ × 48
Area Of Triangle = 24