Triangles on the Same Base and between the Same Parallels

Q. ABCD is a rectangle of area $40c{m}^2$. If X is any point on AB, what is the area of $\Delta XCD$?
[1 Mark]

Q.

In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:

1. 16 cm²

2. 26 cm²

3. 36 cm²

4. 46 cm²

Q.

Two triangles have equal area of $24c{m}^2$ and stand on the same base of 6 cm, if the distance PQ (on base) between their altitudes is equal to the length of one of the altitude. Then the area of quadrilateral formed by the altitudes and the base PQ is equal to:

1. 34 cm²

2. 44 cm²

3. 54 cm²

4. 64 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.

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then area of($△$BPC) equal to

1. area of(ΔBPC) = (1/3) area of (ΔDPQ)

2. area of(ΔBPC) = (3/8) area of (ΔDPQ)

3. area of (ΔBPC) = (1/4) area of (ΔDPQ)

4. area of (ΔBPC) = area of (ΔDPQ)

Q.

In a given figure, BE is a median of $△ABD$. If the area of parallelogram ABCD is $24c{m}^2$. Then the area of $△ABE$ is:

1. $6c{m}^2$

2. $8c{m}^2$

3. $12c{m}^2$

4. $10c{m}^2$

Q.
In the figure given above, the ratio $\frac{AreaofDPQC}{AreaofABCD}$ =____.

1. 1
2. $\frac{1}{2}$
3. $\frac{2}{3}$
4. $\frac{1}{3}$

Q.

Here AB $\parallel$ CD. If the altitude of $△$ACD is 6 cm and CD is 8 cm then the area of $△$BCD is:

1. $14c{m}^2$
2. $24c{m}^2$
3. $34c{m}^2$
4. $44c{m}^2$

Q.

The given figure shows parallelogram ABCD. Points P and Q trisect the side AB, then which of the following is correct?

1. Area of $△$DPQ = $\frac{1}{3}$ Area of (parallelogram ABCD)
2. Area of $△$DPQ = $\frac{4}{5}$ Area of (parallelogram ABCD)
3. Area of $△$DPQ = $\frac{2}{5}$ Area of (parallelogram ABCD)
4. Area of $△$DPQ = $\frac{1}{6}$ Area of (parallelogram ABCD)

Q.

If two triangles have equal area and stand on the same base, then the altitudes of the triangle are equal.

1. True

2. False