Question

Find the missing values:
Base
Height
Area of Triangle
15 cm
87 cm
31.4 mm
1256 mm
22 cm
170.5 cm
PQRS is a parallelogram (Fig 11.23). QM is the height from Q
to SR and QN is the height from Q to PS. If SR = 12 cm and
QM=7.6 cm. Find:
(a) the area of the parallegram PQRS (b) QN, if PS = 8 cm​

Answer 1

Question :

Find the missing values:

Given :

• Base - 15 cm
• Height - ?
• Area of Triangle - 87 cm²

Solution :

${ \tt Area \: of \: triangle = \dfrac{1}{2} \times base \times height }$

                        ${ \tt 87 = \dfrac{1}{2} \times 15 \times height }$

                 ${ \tt Height = \dfrac{87 \times 2}{15} }$

                              ${ \tt = \dfrac{174}{15} }$

                              ${\tt = 11.6 \: cm}$

Therefore, the Height of the Triangle is 11.6 cm

                         

Given :

• Base - ?
• Height - 31.4 mm
• Area of Triangle - 1256 mm²

Solution :

${ \tt Area \: of \: triangle = \dfrac{1}{2} \times base \times height }$

                    ${ \tt 1256 = \dfrac{1}{2} \times base \times 31.4 }$

                    ${ \tt Base = \dfrac{1256 \times 2}{31.4} }$

                             ${ \tt = \dfrac{2512}{31.4} }$

                             = 80 mm

Therefore, the Base of the Triangle is 80 mm.

Given :

• Base - 22 cm
• Height - ?
• Area of Triangle - 170.5 cm²

Solution :

${ \tt Area \: of \: triangle = \dfrac{1}{2} \times base \times height }$

                   ${ \tt 170.5 = \dfrac{1}{2} \times 22 \times height }$

                ${ \tt Height = \dfrac{170.5 \times 2}{22} }$

                            ${ \tt = \dfrac{341}{22} }$

                            = 15.5 cm

Therefore, the Height of the Triangle is 15.5 cm.

Question :

PQRS is a parallelogram (Fig 11.23). QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm.

Find:  

(a) The area of the parallelogram PQRS

Area of Parallelogram = b × h

                                     = SR × QM

                                     = 12 × 7.6

                                     = 91.2 cm²

Therefore, the Area of the Parallelogram is 91.2 cm².

(b) QN, if PS = 8 cm

Here, we have to find the Height. And here, Area is 91.2 cm².

91.2 = Base × Height

       = 8 × Height

       = 91.2 ÷ 8

       = 11.4 cm

Therefore, QN is 11.4 cm.