Area of triangle given its vertices

Q.

If 2 triangles have the same height, the ratio of their areas is equal to the

1. Ratio of any 2 sides

2. Ratio of their corresponding bases

3. The ratio of their heights

4. 1

Q. What is the area of the right-angled triangle $\Delta MNO$, right angled at N.

1. $\frac{1}{2}\times MO\times NO$
2. $\frac{1}{2}\times MN\times NO$
3. $\frac{1}{2}\times MN\times MO$
4. $MN\times NO$

Q.

The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

1. 30 sq. units

2. 28 sq. units

3. 26 sq. units

4. 27 sq. units

Q. If D $(\frac{-1}{2},\frac{5}{2})$, E (7, 3) and F $(\frac{7}{2},\frac{7}{2})$ are the midpoints of sides of $\Delta$ ABC, find the area of the $\Delta$ ABC.

Q. If $A(-7,5),B(-6,-7),C(-3,-8)$ and $D(2,3)$ are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.

Q. Find the area of the quadrilateral whose vertices taken in order, are $(-4,-2),(-3,-5),(3,-2)$ and $(2,3)$.

Q. If the vertices of a triangle are A(-a, b), B(-a, c) and C(a, c), then the area of triangle = sq units.

1. b(a-c)
2. a(c-b)
3. c(b-a)

Q. The quadrilateral with vertices A(-1, -2), B(1, 0), C(-1, 2) and D(-3, 0) is a .

1. square
2. rhombus
3. rectangle

Q.

What is the area of a triangle whose vertices are (a , b + c), (a, b - c) and (-a, c)?

1. 2ab

2. 4ac

3. 2ac

4. 4ab

Q.

A(a, b), B(c, d) and C(e, f) are the vertices of a triangle.
i) AB + BC > AC
ii) Area of the triangle = $\left(\frac{1}{2}\right)$[a(c-e)+c(f-b)+e(b-d)]
Which of the following are true?

1. Only (ii) is true

2. Only (i) is true

3. Both (i) and (ii) is true

4. Neither (i) nor (ii) is true

Q.

Refer to the following figure. If we were given the coordinates of A, E and B and the lengths of ED, DC and BC, how would you go about finding the area of this figure, pick the easiest way.

1. Break the fig. into $\Delta$AEB and trapezium EBCD

2. Break the fig. into $\Delta$AEB, $\Delta$EAB and $\Delta$BDC

3. Break the fig. into trapeziums EDAX and AXCB where X is
   a point on DC such that AX is perpendicular to AX.

4. Cant say

Q.

Find the area of the figure:

1. 24
2. 27
3. 26
4. 25

Q. P(x, y), A(3, 4) and B (5, -2) are the vertices of triangle PAB such that |PA|=|PB| and area of $\Delta PAB=10$ sq. units, then $PA=k\sqrt{5}$ units. Find the value of k.

1. 2
2. 1
3. $\sqrt{5}$
4. 3

Q. Find the area and match the pair.

1. 47.5 square units
2. 72 square units
3. 10.5 square units

Q. Find the area of the quadrilateral (in sq. units) whose vertices taken in the order are $A(-3,2),B(5,4),C(7,-6)$ and $D(-5,-4)$.