## RS Aggarwal Class 9 Solutions Chapter 7 Areas Ex 7A

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Class 9 Solutions Chapter 7 Areas Ex 7A.

**Question 1.**

**Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.**

**Solution:**

Base of the triangle (b) = 24cm and height (h) = 14.5 cm

∴ Area = x b x h = x 24 x 14.5 cm²

= 174 cm² Ans.

**Question 2.**

**The base of triangular field is three times its altitude. If the cost of sowing the field at Rs. 58 per hectare is Rs. 783, find its base and the height.**

**Solution:**

Let the length of altitude of the triangular field = x then its base = 3x.

**Question 3.**

**Find the area of the triangle whose sides are 42cm, 34 cm and 20cm in length. Hence, find the height corresponding to longest side.**

**Solution:**

Sides of a triangle = 42cm, 34cm and 20cm

Let a = 42cm, b = 34cm and c = 20 cm

**Question 4.**

**Calculate the area of the triangle whose sides are 18cm, 24cm and 30cm in length. Also, find the length of the altitude corresponding to the smallest side.**

**Solution:**

Sides of the triangle = 18cm, 24cm and 30cm

Let a = 18 cm, b = 24 cm and c = 30cm

**Question 5.**

**Find the area of a triangular field whose sides are 91m, 98m and 105m in length. Find the height corresponding to the longest side?**

**Solution:**

Sides of triangular field ABC arc 91m, 98m and 105m

Let AC be the longest side

∴ BD⊥AC

Here a = 98m, b = 105m and c = 91m

**Question 6.**

**The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 150m. Find the area of the triangle.**

**Solution:**

Perimeter of triangle = 150m

Ratio in the sides = 5:12:13

Let sides be 5x, 12x and 13x

**Question 7.**

**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. Also, find the cost of ploughing the field at Rs. 18.80 per 10m².**

**Solution:**

Perimeter of a triangular field = 540m

Ratio is its sides = 25 : 17 : 12

**Question 8.**

**Two sides of a triangular field are 85 m and 154m in length and its perimeter is 324 m. Find (i) the area of the field and (ii) The length of the perpendicular from the opposite vertex on the side measuring 154m.**

**Solution:**

Perimeter of the triangular field = 324 m

Length of the sides are 85m and 154m

**Question 9.**

**Find the area of an isosceles triangle each of whose equal sides measures 13cm and whose base measures 20cm.**

**Solution:**

Length of sides are

13 cm, 13 cm and 20cm

**Question 10.**

**The base of an isosceles triangle measures 80 cm and its area is 360 cm² . Find the perimeter of the triangle.**

**Solution:**

Base of the isosceles triangle ABC = 80cm

Area = 360 cm²

**Question 11.**

**The perimeter of an isosceles triangle is 42cm and its base is 1 times each of the equal sides Find**

**(i) the length of each side of the triangle,**

**(ii) the area of the triangle,**

**(iii) the height of the triangle,**

**Solution:**

Perimeter of the triangle

ABC = 42 cm.

Let length of each equal sides = x

**Question 12.**

**If the area of an equilateral triangle is 36√3 cm², find its perimeter.**

**Solution:**

Area of equilateral triangle = 36√3 cm².

Let length of each side = a

**Question 13.**

**If the area of an equilateral triangle is 81√3 cm²,find its height.**

**Solution:**

Area of equilateral triangle = 81√3 cm²

Let length of each side = a

**Question 14.**

**The base of a right-angled triangle measures 48cm and its hypotenuses measures 50cm. Find the area of the triangle.**

**Solution:**

∆ ABC is a right angled triangle, right angle at B.

∴ BC 48cm and AC = 50cm

**Question 15.**

**Each side of an equilateral triangle measures 8cm. Find (i) the area of the triangle, correct to 2 places of decimal and (ii) the height of the triangle correct to 2 places of decimal. Take √3 = 1.732**

**Solution:**

Each side of equilateral triangle

(a) = 8cm.

**Question 16.**

**The height of an equilateral triangle measures 9 cm Find its area correct to 2 places of decimal. Take √3 = 1.732**

**Solution:**

Let a be the each side of

the equilateral triangle.

**Question 17.**

**An umbrella is made by stitching 12 triangular pieces of cloth, each measuring (50cm x 20cm x 50cm). Find the area of the cloth used in it.**

**Solution:**

The given umbrella has 12 triangular pieces of the size 50cm x 20cm x 50cm. We see that each piece is of an isosceles triangle shape and we have to find firstly area of one such triangle.

**Question 18.**

**A floral design on a floor is made up of 16 tiles, each triangular in shape having sides 16cm, 12cm and 20cm. Find the cost of polishing the tiles at Re.. 1 per sq. cm.**

**Solution:**

The given floral design is made of 16 tiles

The size of each tile is 16cm 12cm, 20cm

Now we have to find the area of firstly one tile

**Question 19.**

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

**Solution:**

**Question 20.**

**Find the perimeter and area of the quadrilateral ABCD in which AB=42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and ∠CBD = 90°.**

**Solution:**

In the figure, ABCD is a quadrilateral

AB = 42 cm, BC = 21 cm, CD = 29 cm,

DA = 34 cm and ∠CBD = 90°

**Question 21.**

**Find the area of quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and ∆BCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral. [Given: √3 = 1.732]**

**Solution:**

from the figure

∆DAB

**Question 22.**

**Find the are of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm**

**Solution:**

**Question 23.**

**Find the area of a parallelogram ABCD in which AB = 14 cm, BC = 10 cm and AC = 16 cm. [Given: √3 = 1.732]**

**Solution:**

from the figure,

We know that

**Question 24.**

**In the given figure ABCD is a quadrilateral in which diagonal BD = 64 cm, AL ⊥BD and CM ⊥ BD such that AL = 16.8 cm and CM = 13.2 cm. Calculate the area of quadrilateral ABCD.**

**Solution:**

Hope given RS Aggarwal Class 9 Solutions Chapter 7 Areas Ex 7A are helpful to complete your math homework.

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