Scroll:Measurement >> Area of Triangle >> ps (1313)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  



1cm
                                                7cm

The figure shows two squares and a shaded triangle. The big square has a length of 7cm and the small square has a length of 1cm.

FInd the shaded area. 

___cm2



Answer:_______________




2)  



1cm
              12cm  

The figure shows two squares and a shaded triangle. The big square has a length of 12cm and the small square has a length of 1cm.

FInd the shaded area. 

___cm2



Answer:_______________




3)  



1cm
                                                6cm

The figure shows two squares and a shaded triangle. The big square has a length of 6cm and the small square has a length of 1cm.

FInd the shaded area. 

___cm2



Answer:_______________




4)  



1cm
              10cm  

The figure shows two squares and a shaded triangle. The big square has a length of 10cm and the small square has a length of 1cm.

FInd the shaded area. 

___cm2



Answer:_______________




5)  



2cm
                                                6cm

The figure shows two squares and a shaded triangle. The big square has a length of 6cm and the small square has a length of 2cm.

FInd the shaded area. 

___cm2



Answer:_______________




6)  



3cm
              8cm  

The figure shows two squares and a shaded triangle. The big square has a length of 8cm and the small square has a length of 3cm.

FInd the shaded area. 

___cm2



Answer:_______________




7)  



1cm
                                                5cm

The figure shows two squares and a shaded triangle. The big square has a length of 5cm and the small square has a length of 1cm.

FInd the shaded area. 

___cm2



Answer:_______________




8)  



4cm
              11cm  

The figure shows two squares and a shaded triangle. The big square has a length of 11cm and the small square has a length of 4cm.

FInd the shaded area. 

___cm2



Answer:_______________




9)  



2cm
                                                7cm

The figure shows two squares and a shaded triangle. The big square has a length of 7cm and the small square has a length of 2cm.

FInd the shaded area. 

___cm2



Answer:_______________




10)  



4cm
              8cm  

The figure shows two squares and a shaded triangle. The big square has a length of 8cm and the small square has a length of 4cm.

FInd the shaded area. 

___cm2



Answer:_______________




 

1)  



1cm
                                                7cm

The figure shows two squares and a shaded triangle. The big square has a length of 7cm and the small square has a length of 1cm.

FInd the shaded area. 

Answer: 9.5cm2



SOLUTION 1 :

 

 

 

 

 

 

1cm

 

 

 
                                                  7cm

 

Step 1: Length of AB → 7cm + 1cm = 8cm

 Step 2: Area of rectangle ABCD → 7cm x 8cm = 56cm2

Step 3: Area of triangle BCH → 12 x 7cm x 7cm = 24.5cm2

Step 4: Area of triangle BAE → 12 x 8cm x 1cm = 4cm2

Step 5: DH = DE

           Height of DE → 7 cm - 1 cm = 6 cm

Step 6: Area of triangle HDE → 12 x 6cm x 6 = 18cm2

Step 7: 24.5cm2 + 4cm2 + 18cm2 = 46.5cm2

Step 8: Area of shaded triangle → 56cm2 - 46.5cm2 = 9.5cm2



2)  



1cm
              12cm  

The figure shows two squares and a shaded triangle. The big square has a length of 12cm and the small square has a length of 1cm.

FInd the shaded area. 

Answer: 17cm2



SOLUTION 1 :

 

 

 

1cm
             12cm  

 

Step 1: Length of AB → 12cm + 1cm

                                   = 13cm

Step 2: Area of rectangle ABCD → 12cm x 13cm

                                                     = 156cm2

Step 3: Area of triangle ADH → 12 x 12cm x 12cm

                                                   = 72cm2

Step 4: Area of triangle ABF → 12 x 13cm x 1cm

                                                  = 6.5cm2

Step 5: CF = CH → 12 cm - 1 cm = 11 cm

Step 6: Area of triangle HCF → 12 x 11cm x 11cm

                                                 = 60.5cm2

Step 7: 72cm2 + 6.5cm2 + 60.5cm2 = 139cm2

Step 8: Area of shaded triangle → 156cm2 - 139cm2

                                                     = 17cm2



3)  



1cm
                                                6cm

The figure shows two squares and a shaded triangle. The big square has a length of 6cm and the small square has a length of 1cm.

FInd the shaded area. 

Answer: 8cm2



SOLUTION 1 :

 

 

 

 

 

 

1cm

 

 

 
                                                  6cm

 

Step 1: Length of AB → 6cm + 1cm = 7cm

 Step 2: Area of rectangle ABCD → 6cm x 7cm = 42cm2

Step 3: Area of triangle BCH → 12 x 6cm x 6cm = 18cm2

Step 4: Area of triangle BAE → 12 x 7cm x 1cm = 3.5cm2

Step 5: DH = DE

           Height of DE → 6 cm - 1 cm = 5 cm

Step 6: Area of triangle HDE → 12 x 5cm x 5 = 12.5cm2

Step 7: 18cm2 + 3.5cm2 + 12.5cm2 = 34cm2

Step 8: Area of shaded triangle → 42cm2 - 34cm2 = 8cm2



4)  



1cm
              10cm  

The figure shows two squares and a shaded triangle. The big square has a length of 10cm and the small square has a length of 1cm.

FInd the shaded area. 

Answer: 14cm2



SOLUTION 1 :

 

 

 

1cm
             10cm  

 

Step 1: Length of AB → 10cm + 1cm

                                   = 11cm

Step 2: Area of rectangle ABCD → 10cm x 11cm

                                                     = 110cm2

Step 3: Area of triangle ADH → 12 x 10cm x 10cm

                                                   = 50cm2

Step 4: Area of triangle ABF → 12 x 11cm x 1cm

                                                  = 5.5cm2

Step 5: CF = CH → 10 cm - 1 cm = 9 cm

Step 6: Area of triangle HCF → 12 x 9cm x 9cm

                                                 = 40.5cm2

Step 7: 50cm2 + 5.5cm2 + 40.5cm2 = 96cm2

Step 8: Area of shaded triangle → 110cm2 - 96cm2

                                                     = 14cm2



5)  



2cm
                                                6cm

The figure shows two squares and a shaded triangle. The big square has a length of 6cm and the small square has a length of 2cm.

FInd the shaded area. 

Answer: 14cm2



SOLUTION 1 :

 

 

 

 

 

 

2cm

 

 

 
                                                  6cm

 

Step 1: Length of AB → 6cm + 2cm = 8cm

 Step 2: Area of rectangle ABCD → 6cm x 8cm = 48cm2

Step 3: Area of triangle BCH → 12 x 6cm x 6cm = 18cm2

Step 4: Area of triangle BAE → 12 x 8cm x 2cm = 8cm2

Step 5: DH = DE

           Height of DE → 6 cm - 2 cm = 4 cm

Step 6: Area of triangle HDE → 12 x 4cm x 4 = 8cm2

Step 7: 18cm2 + 8cm2 + 8cm2 = 34cm2

Step 8: Area of shaded triangle → 48cm2 - 34cm2 = 14cm2



6)  



3cm
              8cm  

The figure shows two squares and a shaded triangle. The big square has a length of 8cm and the small square has a length of 3cm.

FInd the shaded area. 

Answer: 27cm2



SOLUTION 1 :

 

 

 

3cm
             8cm  

 

Step 1: Length of AB → 8cm + 3cm

                                   = 11cm

Step 2: Area of rectangle ABCD → 8cm x 11cm

                                                     = 88cm2

Step 3: Area of triangle ADH → 12 x 8cm x 8cm

                                                   = 32cm2

Step 4: Area of triangle ABF → 12 x 11cm x 3cm

                                                  = 16.5cm2

Step 5: CF = CH → 8 cm - 3 cm = 5 cm

Step 6: Area of triangle HCF → 12 x 5cm x 5cm

                                                 = 12.5cm2

Step 7: 32cm2 + 16.5cm2 + 12.5cm2 = 61cm2

Step 8: Area of shaded triangle → 88cm2 - 61cm2

                                                     = 27cm2



7)  



1cm
                                                5cm

The figure shows two squares and a shaded triangle. The big square has a length of 5cm and the small square has a length of 1cm.

FInd the shaded area. 

Answer: 6.5cm2



SOLUTION 1 :

 

 

 

 

 

 

1cm

 

 

 
                                                  5cm

 

Step 1: Length of AB → 5cm + 1cm = 6cm

 Step 2: Area of rectangle ABCD → 5cm x 6cm = 30cm2

Step 3: Area of triangle BCH → 12 x 5cm x 5cm = 12.5cm2

Step 4: Area of triangle BAE → 12 x 6cm x 1cm = 3cm2

Step 5: DH = DE

           Height of DE → 5 cm - 1 cm = 4 cm

Step 6: Area of triangle HDE → 12 x 4cm x 4 = 8cm2

Step 7: 12.5cm2 + 3cm2 + 8cm2 = 23.5cm2

Step 8: Area of shaded triangle → 30cm2 - 23.5cm2 = 6.5cm2



8)  



4cm
              11cm  

The figure shows two squares and a shaded triangle. The big square has a length of 11cm and the small square has a length of 4cm.

FInd the shaded area. 

Answer: 50cm2



SOLUTION 1 :

 

 

 

4cm
             11cm  

 

Step 1: Length of AB → 11cm + 4cm

                                   = 15cm

Step 2: Area of rectangle ABCD → 11cm x 15cm

                                                     = 165cm2

Step 3: Area of triangle ADH → 12 x 11cm x 11cm

                                                   = 60.5cm2

Step 4: Area of triangle ABF → 12 x 15cm x 4cm

                                                  = 30cm2

Step 5: CF = CH → 11 cm - 4 cm = 7 cm

Step 6: Area of triangle HCF → 12 x 7cm x 7cm

                                                 = 24.5cm2

Step 7: 60.5cm2 + 30cm2 + 24.5cm2 = 115cm2

Step 8: Area of shaded triangle → 165cm2 - 115cm2

                                                     = 50cm2



9)  



2cm
                                                7cm

The figure shows two squares and a shaded triangle. The big square has a length of 7cm and the small square has a length of 2cm.

FInd the shaded area. 

Answer: 17cm2



SOLUTION 1 :

 

 

 

 

 

 

2cm

 

 

 
                                                  7cm

 

Step 1: Length of AB → 7cm + 2cm = 9cm

 Step 2: Area of rectangle ABCD → 7cm x 9cm = 63cm2

Step 3: Area of triangle BCH → 12 x 7cm x 7cm = 24.5cm2

Step 4: Area of triangle BAE → 12 x 9cm x 2cm = 9cm2

Step 5: DH = DE

           Height of DE → 7 cm - 2 cm = 5 cm

Step 6: Area of triangle HDE → 12 x 5cm x 5 = 12.5cm2

Step 7: 24.5cm2 + 9cm2 + 12.5cm2 = 46cm2

Step 8: Area of shaded triangle → 63cm2 - 46cm2 = 17cm2



10)  



4cm
              8cm  

The figure shows two squares and a shaded triangle. The big square has a length of 8cm and the small square has a length of 4cm.

FInd the shaded area. 

Answer: 32cm2



SOLUTION 1 :

 

 

 

4cm
             8cm  

 

Step 1: Length of AB → 8cm + 4cm

                                   = 12cm

Step 2: Area of rectangle ABCD → 8cm x 12cm

                                                     = 96cm2

Step 3: Area of triangle ADH → 12 x 8cm x 8cm

                                                   = 32cm2

Step 4: Area of triangle ABF → 12 x 12cm x 4cm

                                                  = 24cm2

Step 5: CF = CH → 8 cm - 4 cm = 4 cm

Step 6: Area of triangle HCF → 12 x 4cm x 4cm

                                                 = 8cm2

Step 7: 32cm2 + 24cm2 + 8cm2 = 64cm2

Step 8: Area of shaded triangle → 96cm2 - 64cm2

                                                     = 32cm2