Sasi Math (Revised for 1024)

Scroll:Measurement >> Area of Triangle >> ps (1314)

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.

ABCD is a rectangle of area 180cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a square of area 16cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a rectangle of area 120cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a square of area 36cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a rectangle of area 156cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a square of area 100cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a rectangle of area 88cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a square of area 64cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a rectangle of area 176cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

10)

ABCD is a square of area 100cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

cm²

Answer:_______________

ABCD is a rectangle of area 180cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

Answer: 67.5 cm²

SOLUTION 1 :

3 cm

30 cm

Step 1: Area of rectangle ACDE → 30 cm x 6 cm = 180 cm²

Step 2: Length of AB → 30 cm ÷ 2 = 15 cm

Step 3: Lenght of AF → 6 cm ÷ 2 = 3 cm

Step 4: Area of triangle ABF → $\frac{1}{2}$ x 15 cm x 3 cm = 22.5 cm²

Step 5: Area of triangle CDB → $\frac{1}{2}$ x 15 cm x 6 cm = 45 cm²

Step 6: Area of triangle DEF → $\frac{1}{2}$ x 30 cm x 3 cm = 45 cm²

Step 7: 22.5 cm² + 45 cm² + 45 cm² = 112.5cm²

Step 8: Area of shaded triangle → 180 cm² - 112.5 cm² = 67.5 cm²

ABCD is a square of area 16cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

Answer: 6 cm²

SOLUTION 1 :

2 cm

4 cm

Step 1: Area of square ABCD → 4 cm x 4 cm = 16 cm²

Step 2: Length of AF → 4 cm ÷ 2 = 2 cm

Step 3: Area of triangle AFE → $\frac{1}{2}$ x 2 cm x 2 cm = 2 cm²

Step 4: Area of triangle CDE → $\frac{1}{2}$ x 2 cm x 4 cm = 4 cm²

Step 5: Area of triangle CBF → $\frac{1}{2}$ x 2 cm x 4 cm = 4 cm²

Step 6: 2 cm² + 4 cm² + 4 cm² = 10cm²

Step 7: 16 cm² - 10 cm² = 6 cm²

ABCD is a rectangle of area 120cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

Answer: 45 cm²

SOLUTION 1 :

3 cm

20 cm

Step 1: Area of rectangle ACDE → 20 cm x 6 cm = 120 cm²

Step 2: Length of AB → 20 cm ÷ 2 = 10 cm

Step 3: Lenght of AF → 6 cm ÷ 2 = 3 cm

Step 4: Area of triangle ABF → $\frac{1}{2}$ x 10 cm x 3 cm = 15 cm²

Step 5: Area of triangle CDB → $\frac{1}{2}$ x 10 cm x 6 cm = 30 cm²

Step 6: Area of triangle DEF → $\frac{1}{2}$ x 20 cm x 3 cm = 30 cm²

Step 7: 15 cm² + 30 cm² + 30 cm² = 75cm²

Step 8: Area of shaded triangle → 120 cm² - 75 cm² = 45 cm²

ABCD is a square of area 36cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

Answer: 13.5 cm²

SOLUTION 1 :

3 cm

6 cm

Step 1: Area of square ABCD → 6 cm x 6 cm = 36 cm²

Step 2: Length of AF → 6 cm ÷ 2 = 3 cm

Step 3: Area of triangle AFE → $\frac{1}{2}$ x 3 cm x 3 cm = 4.5 cm²

Step 4: Area of triangle CDE → $\frac{1}{2}$ x 3 cm x 6 cm = 9 cm²

Step 5: Area of triangle CBF → $\frac{1}{2}$ x 3 cm x 6 cm = 9 cm²

Step 6: 4.5 cm² + 9 cm² + 9 cm² = 22.5cm²

Step 7: 36 cm² - 22.5 cm² = 13.5 cm²

ABCD is a rectangle of area 156cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

Answer: 58.5 cm²

SOLUTION 1 :

3 cm

26 cm

Step 1: Area of rectangle ACDE → 26 cm x 6 cm = 156 cm²

Step 2: Length of AB → 26 cm ÷ 2 = 13 cm

Step 3: Lenght of AF → 6 cm ÷ 2 = 3 cm

Step 4: Area of triangle ABF → $\frac{1}{2}$ x 13 cm x 3 cm = 19.5 cm²

Step 5: Area of triangle CDB → $\frac{1}{2}$ x 13 cm x 6 cm = 39 cm²

Step 6: Area of triangle DEF → $\frac{1}{2}$ x 26 cm x 3 cm = 39 cm²

Step 7: 19.5 cm² + 39 cm² + 39 cm² = 97.5cm²

Step 8: Area of shaded triangle → 156 cm² - 97.5 cm² = 58.5 cm²

ABCD is a square of area 100cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

Answer: 37.5 cm²

SOLUTION 1 :

5 cm

10 cm

Step 1: Area of square ABCD → 10 cm x 10 cm = 100 cm²

Step 2: Length of AF → 10 cm ÷ 2 = 5 cm

Step 3: Area of triangle AFE → $\frac{1}{2}$ x 5 cm x 5 cm = 12.5 cm²

Step 4: Area of triangle CDE → $\frac{1}{2}$ x 5 cm x 10 cm = 25 cm²

Step 5: Area of triangle CBF → $\frac{1}{2}$ x 5 cm x 10 cm = 25 cm²

Step 6: 12.5 cm² + 25 cm² + 25 cm² = 62.5cm²

Step 7: 100 cm² - 62.5 cm² = 37.5 cm²

ABCD is a rectangle of area 88cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

Answer: 33 cm²

SOLUTION 1 :

2 cm

22 cm

Step 1: Area of rectangle ACDE → 22 cm x 4 cm = 88 cm²

Step 2: Length of AB → 22 cm ÷ 2 = 11 cm

Step 3: Lenght of AF → 4 cm ÷ 2 = 2 cm

Step 4: Area of triangle ABF → $\frac{1}{2}$ x 11 cm x 2 cm = 11 cm²

Step 5: Area of triangle CDB → $\frac{1}{2}$ x 11 cm x 4 cm = 22 cm²

Step 6: Area of triangle DEF → $\frac{1}{2}$ x 22 cm x 2 cm = 22 cm²

Step 7: 11 cm² + 22 cm² + 22 cm² = 55cm²

Step 8: Area of shaded triangle → 88 cm² - 55 cm² = 33 cm²

ABCD is a square of area 64cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

Answer: 24 cm²

SOLUTION 1 :

4 cm

8 cm

Step 1: Area of square ABCD → 8 cm x 8 cm = 64 cm²

Step 2: Length of AF → 8 cm ÷ 2 = 4 cm

Step 3: Area of triangle AFE → $\frac{1}{2}$ x 4 cm x 4 cm = 8 cm²

Step 4: Area of triangle CDE → $\frac{1}{2}$ x 4 cm x 8 cm = 16 cm²

Step 5: Area of triangle CBF → $\frac{1}{2}$ x 4 cm x 8 cm = 16 cm²

Step 6: 8 cm² + 16 cm² + 16 cm² = 40cm²

Step 7: 64 cm² - 40 cm² = 24 cm²

ABCD is a rectangle of area 176cm² . B and F are midpoints of AC and AE respectively.

Find the area of the shaded triangle.

Answer: 66 cm²

SOLUTION 1 :

4 cm

22 cm

Step 1: Area of rectangle ACDE → 22 cm x 8 cm = 176 cm²

Step 2: Length of AB → 22 cm ÷ 2 = 11 cm

Step 3: Lenght of AF → 8 cm ÷ 2 = 4 cm

Step 4: Area of triangle ABF → $\frac{1}{2}$ x 11 cm x 4 cm = 22 cm²

Step 5: Area of triangle CDB → $\frac{1}{2}$ x 11 cm x 8 cm = 44 cm²

Step 6: Area of triangle DEF → $\frac{1}{2}$ x 22 cm x 4 cm = 44 cm²

Step 7: 22 cm² + 44 cm² + 44 cm² = 110cm²

Step 8: Area of shaded triangle → 176 cm² - 110 cm² = 66 cm²

10)

ABCD is a square of area 100cm² . E and F are midpoints of AD and AB respectively.

Find the area of the shaded triangle.

Answer: 37.5 cm²

SOLUTION 1 :

5 cm

10 cm

Step 1: Area of square ABCD → 10 cm x 10 cm = 100 cm²

Step 2: Length of AF → 10 cm ÷ 2 = 5 cm

Step 3: Area of triangle AFE → $\frac{1}{2}$ x 5 cm x 5 cm = 12.5 cm²

Step 4: Area of triangle CDE → $\frac{1}{2}$ x 5 cm x 10 cm = 25 cm²

Step 5: Area of triangle CBF → $\frac{1}{2}$ x 5 cm x 10 cm = 25 cm²

Step 6: 12.5 cm² + 25 cm² + 25 cm² = 62.5cm²

Step 7: 100 cm² - 62.5 cm² = 37.5 cm²