Question

(C) 6 cm
(D) 75 cm
2. [AS1] In a parallelogram ABCD, AB = 12 cm and AD = 18 cm. AE and AF are the altitudes from A
on to CD and BC respectively such that AE = 15 cm. Then AF =
(A) 10 cm
(B) 227 cm
(C) 30 cm
(D) 15 cm
3. [AS1] I gm ABCD and l em APOD lie on the same base. The common base of these​

Answer 1

Given:-

AB = 12 cm

AD = 18 cm

AE and AF are altitudes from A on to CD and BC respectively.

AE = 15 cm

Solution:-

Here, Area of Parallelogram = Base × Height

Now, Area of Parallelogram ABCD ⇒ Base × Height

                                                          ⇒ 12 cm × 15 cm

                                                          ⇒ 180 cm²

We know that the area of the Parallelogram ABCD will be same if the base and height will change.

Since, Area of Parallelogram ABCD ⇒ Base × Height

                                            180 cm² ⇒ 18 cm × h

                                             $\dfrac{180 cm^{2}}{18 cm}$  ⇒ h

                                                       h ⇒ 10 cm

∴ Height is equal to 10 cm.

Hence, AF is equal to 10 cm.

So, Option (A) is correct.

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(2,4)\qbezier(2,4)(1.6,4)(7,4)\qbezier(6,1)(6,1)(7,4)\qbezier(2,4)(2,4)(2,1)\qbezier(2,4)(1.6,4)(6.5,2.5)\put(0.7,0.5){\sf B}\put(6,0.5){\sf C}\put(1.8,4.3){\sf A}\put(7,4.3){\sf D}\put(2,0.5){\sf E}\put(3.3,0.5){\sf 12 cm}\put(6.7,1.5){\sf 18 cm}\put(6.8,2.4){\sf F}\put(2.2,2.2){\sf 15 cm}\end{picture}$

Some important terms:-

• Area of Parallelogram = Base × Height

• Perimeter of Parallelogram = 2 ( a + b )