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9th CBSE

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The sides of a triangular plot are in the ratio of $6 : 7 : 8$ and its perimeter is $420 m$ . Find its area.

Important Questions on Heron's Formula

HARD

9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 8

A farmer has a triangular field with sides

240 m

200 m

and

360 m

, where he grew wheat. In another triangular field with sides

240 m

320 m

and

400 m

adjacent to the previous field, he wanted to grow potatoes and onions (see figure). He divided the field into two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions?
Question Image

Note:

10,000 m^{2} = 1 h e c t a r e

HARD

9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 9

Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes

A B

B C

and

C A

; while the other through

A C

C D

and

D A

(see figure). Then they cleaned the area enclosed within their lanes. If

A B = 9 m

B C = 40 m

C D = 15 m

D A = 28 m

and

∠ B = 90 °

, Which group cleaned more area and by how much? Find the total area cleaned by the students (neglecting the width of the lanes).
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MEDIUM

9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 10

Parul has a piece of land which is in the shape of a rhombus (see fig.). She wants her daughter and son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is

400 m

and one of the diagonal is

160 m

, how much area each of them will get for their crops?
Question Image

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 11

Find the height of a trapezium in which parallel sides are

25 c m

and

77 c m

and non-parallel sides and

26 c m

and

60 c m

. Given the area of the trapezium as

1644 c m^{2}

MEDIUM

9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 1

The base of a right triangle is

8 c m

and hypotenuse is

10 c m

. What is the area of the triangle?

MEDIUM

9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 2

The sides of a triangle are

5 c m, 12 c m

and

13 c m

. What is the area of the triangle?

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 3

What is the area of the given $∆ A B C$ ?

Question Image

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9th CBSE

IMPORTANT

Full Marks Mathematics 9>Chapter 12 - Heron's Formula>TEST YOUR SKILLS>Q 4

The sides of a triangle are in the ratio of

3 : 4 : 5

and its perimeter is

510 m

. What is the measure of its greatest side?

The sides of a triangular plot are in the ratio of 6:7:8 and its perimeter is 420 m. Find its area.

Important Questions on Heron's Formula

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The sides of a triangular plot are in the ratio of $6 : 7 : 8$ and its perimeter is $420 m$ . Find its area.