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In a quadrilateral ABCD, the length of diagonal AC is 28 cm. The length of perpendicular from B and D on AC are 7 cm and 9 cm respectively. Then, the area of ABCD is:
- a)264
- b)224
- c)324
- d)214
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a quadrilateral ABCD, the length of diagonal AC is 28 cm. The leng...
Area of quadrilateral ABCD = Ar . Of ΔADC + Ar . Of ΔABC
Hence the correct answer is option (b).
Most Upvoted Answer
In a quadrilateral ABCD, the length of diagonal AC is 28 cm. The leng...
Solution:
Given, AC = 28 cm, BD ⊥ AC, BD ⊥ AC at B and D respectively such that BD = 9 cm and DC = 7 cm.
Let us draw the diagonal BD and join AD and BC.
From the right-angled triangle ABD, we have:
AB^2 + BD^2 = AD^2
AB^2 + 81 = AD^2 …… (1)
From the right-angled triangle BCD, we have:
BC^2 + CD^2 = BD^2
BC^2 + 49 = 81
BC^2 = 32
BC = √32
Now, we have the length of all the four sides of the quadrilateral ABCD:
AB^2 + AD^2 = AC^2
AB^2 + (AB^2 + 81) = 28^2
2AB^2 = 28^2 - 81
AB^2 = 343
AB = √343 = 7√7
Area of quadrilateral ABCD = Area of ΔABD + Area of ΔBCD
Area of ΔABD = 1/2 × AB × BD = 1/2 × 7√7 × 9 = 63√7/2
Area of ΔBCD = 1/2 × BC × CD = 1/2 × √32 × 7 = 7√2
Area of quadrilateral ABCD = 63√7/2 + 7√2 = (63√7 + 14√2)/2 = 224 cm^2
Therefore, the area of ABCD is 224 cm^2.
Given, AC = 28 cm, BD ⊥ AC, BD ⊥ AC at B and D respectively such that BD = 9 cm and DC = 7 cm.
Let us draw the diagonal BD and join AD and BC.
From the right-angled triangle ABD, we have:
AB^2 + BD^2 = AD^2
AB^2 + 81 = AD^2 …… (1)
From the right-angled triangle BCD, we have:
BC^2 + CD^2 = BD^2
BC^2 + 49 = 81
BC^2 = 32
BC = √32
Now, we have the length of all the four sides of the quadrilateral ABCD:
AB^2 + AD^2 = AC^2
AB^2 + (AB^2 + 81) = 28^2
2AB^2 = 28^2 - 81
AB^2 = 343
AB = √343 = 7√7
Area of quadrilateral ABCD = Area of ΔABD + Area of ΔBCD
Area of ΔABD = 1/2 × AB × BD = 1/2 × 7√7 × 9 = 63√7/2
Area of ΔBCD = 1/2 × BC × CD = 1/2 × √32 × 7 = 7√2
Area of quadrilateral ABCD = 63√7/2 + 7√2 = (63√7 + 14√2)/2 = 224 cm^2
Therefore, the area of ABCD is 224 cm^2.
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In a quadrilateral ABCD, the length of diagonal AC is 28 cm. The length of perpendicular from B and D on AC are 7 cm and 9 cm respectively. Then, the area of ABCD is:a)264b)224c)324d)214Correct answer is option 'B'. Can you explain this answer?
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