IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 5

MEDIUM

9th Foundation

IMPORTANT

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A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are $26 cm, 28 cm and 30 cm$ , and the parallelogram stands on the base $28 cm$ , find the height of the parallelogram.

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Important Questions on Heron's Formula

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 6

In the given parallelogram, find the length of the altitude from vertex

A

on the side

D C

.

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MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 7

A rhombus shaped sheet with perimeter

40 cm

and one diagonal

12 cm,

is painted on both sides at the rate of

₹ 5 per {cm}^{2}

. Find the cost of painting.

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 8

The area of a triangle, two sides of which are

8 cm

and

11 cm

and the perimeter is

32 cm

is

k \sqrt{30} {cm}^{2}

. Find the value of k.

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 9

In the given figure,

∆ ABC

has sides

AB = 7 .5 cm, AC = 6 .5 cm and BC = 7 cm .

On base

BC

a parallelogram

DBCE

of same area as that of

∆ ABC

is constructed. Find the height

DF

of the parallelogram.
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Question Image

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 10

The sides of a triangle are

11 cm, 15 cm

and

16 cm

. The altitude to the largest side is ______.

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 11

A field is in the shape of a trapezium whose parallel sides are

25 m

and

10 m

. The non-parallel sides are

14 m

and

13 m

. Find the area of the field.

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 12

Find the cost of laying grass in a triangular field of sides

50 m, 65 m and 65 m

at the rate of ₹

7 per m^{2}

.

MEDIUM

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 12 - Heron's Formula>MATHEMATICAL REASONING>Q 13

The base of an isosceles triangle measures

24 cm

and its area is

192 {cm}^{2}

. Find its perimeter.