**Exercise 12.1**

**Question 1: Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm.**

**Solution:**

**Question 2: Find the area of a triangle whose sides are respectively 9 cm, 12 cm and 15 cm.**

**Solution:**

**Question 3: Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.**

**Solution:**

**Question 4: In a triangle ABC, AB = 15cm, BC = 13cm and AC = 14cm. Find the area of triangle ABC and hence its altitude on AC.**

**Solution:**

**Question 5: The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle.**

**Solution:**

**Question 6: The perimeter of a triangle is 300 m. If its sides are in the ratio of 3: 5: 7. Find the area of the triangle.**

**Solution:**

**Question 7: The perimeter of a triangular field is 240dm. If two of its sides are 78dm and 50dm, find the length of the perpendicular on the side of length 50dm from the opposite vertex.**

**Solution:**

**Question 8: A triangle has sides 35 cm, 54 cm, 61 cm long. Find its area. Also, find the smallest of its altitudes?**

**Solution:**

^{2}= 1/2 × H × 61

**Question 9: The lengths of the sides of a triangle are in a ratio of 3: 4: 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side?**

**Solution:**

**Question 10: The perimeter of an isosceles triangle is 42 cm and its base is 3/2 times each of the equal side. Find the length of each of the triangle, area of the triangle and the height of the triangle.**

**Solution:**

**Question 11: Find the area of the shaded region in fig. below.**

**Solution:**

^{2}= AD

^{2}+ BD

^{2 }

^{2}= 12

^{2}+ 16

^{2}

^{2}= 400cm2

^{2}= √(400cm

^{2})

**Exercise 12.2**

**Question 1: Find the area of the quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.**

**Solution:**

^{2}

^{2}= AB

^{2}+ BC

^{2}

^{2}= (3)

^{2}+ (4)

^{2}

^{2}= 9 + 16

^{2}= 25

**Question 2: The sides of a quadrilateral field, taken in order are 26m, 27m, 7m, and 24m respectively. The angle contained by the last two sides is a right angle. Find its area.**

**Solution:**

^{2}= AD

^{2}+ CD

^{2}

^{2}= (24)

^{2}+ (7)

^{2}

^{2}= 576 + 49

^{2}= 625

^{2}

^{2}+ 84 m

^{2}

^{2}

**Question 3: The sides of a quadrilateral, taken in order as 5, 12, 14, 15 meters respectively, and the angle contained by first two sides is a right angle. Find its area.**

**Solution:**

^{2}

^{2}= AB

^{2}+ BC

^{2}

^{2}= (5)

^{2}+ (12)

^{2}

^{2}= 25 + 144

**Question 4: A park in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m. How much area does it occupy?**

**Solution:**

^{2}= BC

^{2}+ CD

^{2}

^{2}= 12

^{2}+ 5

^{2 }

^{2}= 144 + 25

^{2}= 169

^{2}

**Question 5: Two parallel sides of a trapezium are 60 m and 77 m and the other sides are 25 m and 26 m. Find the area of the trapezium.**

**Solution:**

It is given that,

AB = 77m

CD = 60 m

BC = 26m

AD = 25m

AE and CF are diagonals.

DE and CF are two perpendiculars on AB.

DC = EF = 60 m

Let us assumed that, AE = x

BF = 77 – (60 + x)

BF = 17 – x

In ∆ADE,

**Question 6: Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.**

**Solution:**

^{2}= AB

^{2}− OA

^{2 }

^{2}= 20

^{2}−12

^{2 }

^{2}= 400 – 144

^{2}= 256

^{2}= √256

^{2}

**Question 7: A rhombus sheet, whose perimeter is 32 m and whose diagonal is 10 m long, is painted on both the sides at the rate of Rs 5 per m**

^{2}. Find the cost of painting.**Solution:**

^{2}= AB

^{2}− OA

^{2}

^{2}= 8

^{2}– 5

^{2}

^{2}= 64 – 25

^{2}= 39

^{2}

^{2}

**Question 8: Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. [Take √3 = 1.73]**

**Solution:**

^{2}= BD

^{2}− AD

^{2}

^{2}= 26

^{2}- 24

^{2}

^{2 }

^{2}

^{2}

**Question 9: Find the area of quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and the diagonal BD = 20 cm.**

**Solution:**

**Question 10: Find the perimeter and the area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, AC = 15 cm and angle ACB = 90°.**

**Solution:**

^{2}= AB

^{2}− AC

^{2}

^{2}= 17

^{2}− 15

^{2}

^{2}= 289 − 225

^{2}

^{2}+ 54 cm

^{2}

^{2}

**Question 11: The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of parallelogram.**

**Solution:**

^{2}

^{2}

**Question 12: Find the area of the blades of the magnetic compass shown in figure given below:**

**Solution:**

^{2}

**Question 13: A hand fan is made by sticking 10 equal size triangular strips of two different types of paper as shown in the figure. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.**

**Solution:**

^{2}

^{2}

**Question 14: A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of a parallelogram.**

**Solution:**

**Exercise VSAQs**

**Question 1: Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.**

**Solution:**

**Question 2: Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.**

**Solution:**

**Question 3: Find the area of an isosceles triangle having the base x cm and one side y cm.**

**Solution:**

**Question 4: Find the area of an equilateral triangle having each side 4 cm.**

**Solution:**

^{2}

**Question 5: Find the area of an equilateral triangle having each side x cm.**

**Solution:**

^{2}