Question

A
2. In the adjoining figure
Find the area of the triangle ABC given that
AD = 5 cm, BC = 4 cm.
Given that the area of ABC is 12 cm2 and
AC = 8 cm. Find BE.
(ii) Given that AB = 4 cm, CF = 6 cm and AD = 8 cm
find BC.
E
F
C с
B
D​

Answer 1

Answer:

ss 9 Math are prepared by experts and are 100% accurate.

Page No 387:

Question 1:

Which of the following figures lie on the same base and between the same parallels. In such a case, write the comon base and the two parallels.

ANSWER:

(i) No, it doesnt lie on the same base and between the same parallels.

(ii) No, it doesnt lie on the same base and between the same parallels.

(iii) Yes, it lies on the same base and between the same parallels. The same base is AB and the parallels are AB and DE.

(iv) No, it doesnt lie on the same base and between the same parallels.

(v) Yes, it lies on the same base and between the same parallels. The same base is BC and the parallels are BC and AD.

(vi) Yes, it lies on the same base and between the same parallels. The same base is CD and the parallels are CD and BP.

Page No 387:

Question 2:

In the adjoining figure, show that ABCD is a parallelogram.

Calculate the area of || gm ABCD.

ANSWER:

Given: A quadrilateral ABCD and BD is a diagonal.

To prove: ABCD is a parallelogram.

Construction: Draw AM ⊥ DC and CL ⊥ AB (extend DC and AB). Join AC, the other diagonal of ABCD.

Proof: ar(quad. ABCD) = ar(∆ABD) + ar(∆DCB)

= 2 ar(∆ABD) [∵ ar(∆ABD) = ar(∆DCB)]

∴ ar(∆ABD) = 12ar(quad. ABCD) ...(i)

Again, ar(quad. ABCD) = ar(∆ABC) + ar(∆CDA)

= 2 ar(∆ ABC) [∵ ar(∆ABC) = ar(∆CDA)]

∴ ar(∆ABC) = 12ar(quad. ABCD) ...(ii)

From (i) and (ii), we have:

ar(∆ABD) = ar(∆ABC) = 12 AB ⨯ BD = 12 AB ⨯ CL

⇒ CL = BD

⇒ DC || AB

Similarly, AD || BC.

Hence, ABCD is a paralleogram.

∴ ar(|| gm ABCD) = base ⨯ height = 5 ⨯ 7 = 35 cm2