Line from Vertex Divides the Length of Opposite Side and Area

Q.

In ∆ABC, D, E and F are respectively mid points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm respectively, the perimeter of ∆DEF will be

1. 15 cm

2. 19 cm

3. 20 cm

4. 12 cm

Q.

If $\mathrm{A}$ is the area of a right-angled triangle and $\mathrm{B}$ is one of the sides containing the right angle, then calculate the length of altitude on the hypotenuse?

Q.

The perimeter of a right angled triangle is $30cm.$ If the hypotenuse is $13cm,$find its area using Herons formula.

Q.

The perimeter of a right angled triangle is $60cm$ and its hypotenuse is $25cm.$ Find the area of the triangle.

Q. If each side of a triangle is doubled, t hen find the ratio of area of the new triangle they formedand the original triangle

Q. Each side of square ABCD has length 1 unit. P and Q are points on AB and DA respectively such that area of triangle APQ is 2 units. Find angle PCQ.

Q. In square ABCD, P and Q are mid-point of AB and CD respectively. If AB = 8cm and PQ and BD intersect at O, then find area of ΔOPB.

Q. D and E are the mid point of the sides AB and AC of a triangle ABC. Then find the ratio of the areas of the triangle ADE and ABC.

Q. 79. Find the area of quidrilateral abcd in which ab=3cm bc=4cm cd=4cm da=5cm ac=5cm

Q. 33. In triangle ABC, AC=3AB.If AD bisects angle A with D lying on BC and E is the foot of the perpendicular from C to AD, then (area of ABC)/(area of CDE) is equal to

Q.

D, E, F are midpoints of sides AB, BC and CA of ∆ABC, if ar(∆ABC) = 64 cm² then, area of ∆BDE is:

1. 12 cm²

2. 16 cm²

3. 32 cm²

4. 8 cm²

Q.

The length of a minute hand of a wall clock is 10 cm. What is the area swept by it in 30 minutes.

1. 7.64

2. 6.50

3. 6.64

4. 6.54

Q. 6. IN A TRIANGLE ABC . XY IS PARALLEL TO AC AND AREA OF TRIANGLE BXY IS EQUAL TO AREA OF QUADRILATERAL XYCA FIND RATION OF SIDE AX/AB

Q. The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.

Q.

What is pi? Why is it used for solving sums in maths?

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

Q.

Find the area of the figure by splitting them into rectangles and squares.

Q.

In the given figure, AC and BD are two diagonals of the rectangle ABCD. They intersect at the point O. The length of the side AD = 8 cm and that of the side DC = 10 cm.

The area of the triangle OCD is

1. 40 cm²

2. 30 cm²

3. 5 cm²

4. 20 cm²

Q.

P and Q are the mid-points of sides AB and BC of triangle ABC respectively and R is the mid-point of AP, then ar ($△$PRQ) is equal to

1. ar ($△$PRQ) = $\frac{2}{3}$ ar ($△$ARC)

2. ar ($△$PRQ) = $\frac{4}{3}$ ar ($△$ARC)

3. ar ($△$PRQ) = $\frac{3}{8}$ ar ($△$ARC)

4. ar ($△$PRQ) = $\frac{1}{2}$ ar ($△$ARC)

Q.

Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

Q. E is a point lying on AB and C is a point lying on FG and ABCD, DEFG are paralle\log rams.If the area ABCD is 100cm^2 , the find the area of DEFG

Q. 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.

Q.

Diagonals AC & BD of a gm ABCD intersect at O. Given that AB = 14 cm & the perpendicular distance between AB & DC is 10 cm, find the area of AOD.

1. 35 sq. cm

2. 140 sq. cm

3. 72 sq. cm

4. 70 sq. cm

Q. AC is parallel to dc area of quadrilateral a b c is equals to 25 square units and area of triangle ABC is equals to 17 square units find area of triangle ACE

Q.

In △ ABC, D is a point on BC such that BD: DC = 2 : 3. If area △ ABD = 10 sq cm, then area of △ ABC = ____ sq cm.

1. 20

2. 25

3. 15

4. 5

Q. 36. Find the area of a traingle , the radius of whose circumcirle is 3 cm and the lenght of the altitude drawm from the opposite vertex to the hypotenuse is 2cm?

Q. In the figure, the diagonals of a trapezium split it into four triangles.

What is the area of the whole trapezium?

Q.

A point D is taken on the side of BC of ∆ABC such that BD = 2DC. Then

1. area (∆ABD) = 2area (∆ADC)

2. area (∆ABD) = area (∆ADC)

3. area (∆ABD) = ¹/₂ area (∆ADC)

4. area (∆ABD) < area (∆ADC)

Q. A point O is taken inside an equilateral ∆ABC. If OL ⊥ BC, OM ⊥ AC and ON ⊥ AB such that OL = 14 cm, OM = 10 cm and ON = 6 cm, find the area of ∆ABC.

Q. The sides of a quadrangular field, taken in order are 26 m, 27 m, 7 m are 24 m respectively. The angle contained by the last two sides is a right angle. Find its area.