Theorem 2: Triangles

Q. ABCD is a parallelogram. P is any point on CD. If ar($△$DPA) = 35 $c{m}^2$ and ar($△$APC) = 15 $c{m}^2$, then area($△$APB) is

1. 15 $c{m}^2$
2. 35 $c{m}^2$
3. 50 $c{m}^2$
4. 70 $c{m}^2$

Q. PQ is a line parallel to side BC and passing through vertex A of a triangle ABC. If BE || AC and CF || AB meet PQ at E and F respectively. If the base and altitude of ΔABC are 6 cm and 8 cm respectively, the area of ΔACF is ___.

1. 48 $c{m}^2$
2. 24 $c{m}^2$
3. 48 $c{m}^2$
4. 12 $c{m}^2$

Q.

In the given figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Then:

1. (Area $\Delta ABP)$ = Area(quad ABCD)

2. (Area $\Delta ABC)$ = Area $\Delta ACP)$

3. (Area $\Delta BCD)$ = Area(quad ACPD)

4. None of these

Q.

In the given figure ABCD is a parallelogram. If area of parallelogram ABCD = 1728 square units, then area $△$ BEC = ____ square units.

1. 864 square units
2. 432 square units
3. 400 square units
4. 1728 square units

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

Q.

If AD is median of ΔABC and P is a point on AC such that ar(ΔADP) : ar(ΔABD) = 2 : 3, then ar(ΔPDC) : ar(ΔABC) is ______ .

1. 2 : 5
2. 3 : 5
3. 1 : 5
4. 1 : 6

Q. If a triangle and parallelogram are on the (P) and between the (Q) then the area of the triangle is (R) the area of the parallelogram.

1. P - different base, Q - different height, R - equal
2. P - same base, Q - same parallels, R - same
3. P - same base, Q - same parallels, R - half
4. P - same base, Q - different height, R - half

Q.

AE || BC and D is the mid-point of BC. If area $△ABC$ = 84 $c{m}^2$, what is area of $△BDE$?

1. 84 $c{m}^2$
2. 42$c{m}^2$
3. 63 $c{m}^2$
4. 21$c{m}^2$

Q. For a parallelogram ABCD, side AB is base for a triangle which is connected to point M on side DC. If the area of parallelogram is $54c{m}^2$. Find the area of $\Delta DMC$

1. $54c{m}^2$
2. $27c{m}^2$
3. $14c{m}^2$
4. $7c{m}^2$

Q.

In the given figure, ABCDE is a pentagon with AC = 5 cm. A line through B parallel to AC meets DC produced at F. If the altitude of triangle ABC (perpendicular to AC) is 6 cm. Find the area of triangle ACF.

1. 5 $c{m}^2$
2. 15 $c{m}^2$
3. 30 $c{m}^2$
4. 10 $c{m}^2$