The area of quadrilateral ABCD whose diagonals are perpendicular and of
lengths 12 cm, 8 cm is
a) 48 cm2
b) 192 cm2
c) 96 cm2
d) 36 cm
HEY GUYZZZ. PLZZ ANSWER ITS REALLY IMP. IT IS MY CURRIERS QUESTIONNN.... PLZZZZZZ
Answers
Step-by-step explanation:
mark brainlist...........
The correct answer is option a) 48 cm².
Given:
A quadrilateral ABCD whose diagonals are perpendicular and of
lengths 12 cm and 8 cm.
To Find:
The area of the quadrilateral ABCD.
Solution:
Let us assume that AC and BD are the diagonals of the quadrilateral ABCD that are perpendicular and meet at point O.
So,
AC = 12 cm and BD = 8 cm.
Hence, the area of quadrilateral ABCD can be seen as the sum of the areas of two triangles, ΔABC and ΔADC that have heights BO and DO respectively.
∴ area of ABCD = area of (ΔABC) + area of (ΔADC)
= (1/2 x AC x BO) + (1/2 x AC x DO) = 1/2 x AC x (BO+OD)
= 1/2 x AC x BD = 1/2 x 12 x 8 = 48 cm².
Hence, the area of quadrilateral ABCD is 48 cm².
∴ The correct answer is option a) 48 cm².
#SPJ2